JEE Advanced Maths Assignment - NARAYANA IIT ...// JEE–Advanced Maths – Assignment Only One...

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JEE–Advanced

Maths – Assignment Only One Correct Answer Type

1. The locus of the orthocenter of the triangle formed by the lines (1+P)x–Py + P(1+P) = 0,

(1+q)x – qy+q(1+q) = 0 and y = 0, where p ≠q, is

(a) a hyperbola (b) a parabola

(c) an ellipse (d) a straight line

2. If two different tangents of y2 = 4x are the normals to x

2 = 4by, then

(a) 1

b2 2

(b) 1

b2 2

(c) 1

b2

(d) 1

b2

3. Minimum distance between the curves 2y x 1 and

2x y 1 is equal to

(a) 3 2

4 (b)

5 2

4

(c) 7

24

(d) 1

24

4. Minimum distance between the curves 2y 4x and

2 2x y 12x 31 0 is equal to

(a) 21 (b) 26

(c) 5 (d) 28

5. Sides of a equilateral ABC touch the parabola 2y 4ax, then point A, B and C lie on

(a) 22y x a 4ax (b)

22y 3 x a ax

(c) 22y 3 x a 4ax (d)

22y x a ax

6. Length of the focal chord of the ellipse 2

2 2

x y1,

a b

that is inclined at an angle with

the x–axis, is equal to

(a) 2

2 2 2 2

2b a

a sin b cos (b)

2

2 2 2 2

2b a

a cos b sin

(c) 2

2 2 2 2

2a b

a sin b cos (d)

2

2 2 2 2

2a b

a cos b sin

7. Eccentricity of the ellipse 2 25x 6xy 5y 8

(a) 1

2 (b)

3

2

(c) 2

3 (d)

1

3

8. PQ is a chord of the ellipse 2 2

2 2

x y1.

a b If O is the centre of the ellipse and eccentric

angle of the points P and Q differ by ,2

then area of triangle OPQ is

(a) ab (b) 2ab

(c) ab / 2 (d) ab / 4


9. An ellipse with major and minor axes of length 10 3 and 10 respectively, slides along

the co-ordinate axes and always remains confined in the first quadrant. The locus of the

centre of the ellipse will be the arc of a circle. The length of this arc will be equal to

(a) 10 units (b) 5 units

(c) 5

4 units (d)

5

3 units

10. Consider a circle 2 2 2x y d and an ellipse

2 2

2 2

x y1,

a b d > maxi. {a,b} from a

variable point P on the circle, tangents PA and PB are drawn to the ellipse. Locus of the

mid–point of chord AB is

(a) 2 2

2 2 4

2 2

x yx y d

a b

(b)

22 2

2 2 2

2 2

x yx y d

a b

(c) 2 2 2 2 4b x a y d (d)

2 2 2 2 4a x b y d

11. PQ is variable chord of the ellipse 2 2

2 2

x y1.

a b if PQ subtend a right angle at the centre

of the ellipse then 2 2

1 1,

OP OQ (O being the origin) is equal to

(a) 2 2

1 1

a b (b)

2 2

2 1

a b

(c) 2 2

1 2

a b (d)

2 2

1 12

a b

12. Consider any chord of the hyperbola xy=c2 that is parallel to the line y = x. Circles are

drawn having this chord as diameter. All these circles will pass through two fixed points

whose co–ordinates are

(a) c 2,c 2 , c 2, c 2 (b) c 2,c 2 , c 2, c 2

(c) c,c , c, c (d) c,c , c,c

13. The tangent at a point ‘P’ on the hyperbola 2 2

2 2

x y1,

a b meets one of its directix at the

point Q. If the line segment PQ subtends an angle at the corresponding focus, than is

always equal to

(a) 4

(b)

2

(c) 3

(d)

6

14. If tangent and normal to the hyperbola xy = c2, at any point ‘P’ cuts off intercept a1 and

a2 on the x–axis respectively and b1 and b2 on the y–axis, then 1 2 1 2a a b b is always

equal to

(a) –1 (b) 1

(c) 0 (d) none of these

15. Locus of the mid–point of the chord of the hyperbola 2 2 2x y a , that touch the

parabola 2y 4ax is

(a) 2x x a y (b) 2y x a y


(c) 3 2x x a y (d) 3 2y x a x

16. Locus of the point of intersection of tangent drawn to the hyperbola 2xy c at the

extremities of any normal chord is

(a) 2

2 2 2x y c xy 0 (b) 2

2 2 2x y c xy 0

(c) 2

2 2 2x y 4c xy 0 (d) 2

2 2 2x y 4c xy 0

17. A water jet from a fountain reaches its maximum height of 4 m at a distance 0.5 m from

the vertical passing through the point O of water outlet. The height of the jet above the

horizontal OX at a distance of 0.75m from the point O is

(a) 5m (b) 6m

(c) 3m (d) 7m

18. Equation of a normal to the curve y = x2–6x + 6 which is perpendicular o the straight line

joining the origin to the vertex of the parabola is

(a) 4x – 4y – 11 = 0 (b) 4x – 4y + 1 = 0

(c) 4x – 4y – 21 = 0 (d) 4x – 4y + 21 = 0

19. A circle drawn on any focal chord of the parabola y2=4ax as diameter cuts parabola at

two points ‘t’ and ‘t’ (other than the extrimity of focal chord) the

(a) tt = –1 (b) tt = 2

(c) tt = 3 (d) none of these

20. Two parabolas with the same axis, focus of each being exterior to the other and the latus

rectum being 4a and 4b. The locus of the middle points of the intercepts between the

parabolas made on the lines parallel to the common axis is a

(a) straight line if a = b (b) parallel line if a ≠ b

(c) parabola for all a, b (d) ellipse if b > a

21. If three distinct normal can be drawn to the parabola y2 – 2y = 4x – 9 from the point

(2a, 0) then range of values of a is

(a) No real values possible (b) (2, )

(c) (– , 2) (d) none of these

22. If the curves 2

2xy 1

4 and

22

2

xy 1

a for suitable value of a cut on four concylic

points, the equation

(a) 2 2x y 2 (b)

2 2x y 1

(c) 2 2x y 4 (d) none of these

23. Angle subtended by common tangents of two ellipse 2

4 x 4 +25y2

= 100 and

2 24 x 1 y 4 at origin is

(a) 3

(b)

4

(c) 2

(d) none of these

24. If PQR be an equilateral triangle inscribed in the auxillary circle of the ellipse 2 2

2 2

x y1

a b (a>b) and PQR be corresponding triangle inscribed within the ellipse then

centriod of the triangle PQR lies at

(a) centre of ellipse (b) focus of ellipse

(c) between focus and centre of major axis (d) none of these


25. The normal at a variable point P on the ellipse 2 2

2 2

x y1

a b , a>b of eccentricity ‘e’ meets

the axes of the ellipse Q and R then the locus of the mid point QR is coinc with a

eccentricity e such that

(a) e is independent of e (b) e = 1

(c) e = e (d) e = 1

e

26. If a variable line x cos ysin P, which is a chord of the hyperbola

2 2

2 2

x y1 b a

a b , subtends a right angle at the centre of the hyperbola then it always

touches a fixed circle whose radius is

(a) ab

b 2a (b)

a

a b

(c) 2 2

ab

b a (d)

ab

b a b

27. Let any double ordinate PNP of the hyperbola 2 2x y

125 16

be produced both sides to

meet the asymptotes in Q and Q, then PQ. PQ is equal to

(a) 25 (b) 16


28. The equation of the line of latus rectum of the rectangular hyperbola xy = c2 is

(a) x y 2c (b) x y 2 2c

(c) x y 2c (d) x y 0

29. The line parallel to the normal to the curve xy = 1 is/are

(a) 3x 4y 5 0 (b) 3x 4y 5 0

(c) 4y 3x 5 0 (d) 3y 4x 5 0

30. The line 22px y 1 p 1 p 1 for different values of p touches

(a) An ellipse of eccentricity 2

3 (b) An ellipse of eccentricity

3

2

(c) Hyperbola of eccentricity 2 (d) none of these

31. If , are the eccentric angels of the ends of a focal chord of the ellipse 2 2

2 2

x y1,

a b

then the eccentricity of the ellipse is

(a)

sin sin

sin

(b)

sin sin

sin

(c)

cos cos

cos

(d)

cos cos

cos

32. If chords of contact of tangents from two points 1 1x , y and 2 2x , y to the ellipse

2 2

2 2

x y1

a b are at right–angle, then 1 2

1 2

x x

y y

(a) 2

2

a

b (b)

2

2

b

a


(c) 4

4

a

b (d)

4

4

b

a

33. PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy = c2

to the asymptotes. The locus of the mid–point of MN is a hyperbola with eccentricity

(a) 2 (b) 2

(c) 1

2 (d) 2 2

34. An ellipse has eccentricity 1

2 and one focus at

1s ,1

2

. Its one directix is the common

tangent, (nearer to S) to the circle 2 2x y 1 and

2 2x y 1. The equation of the

ellipse in standard form is

(a) 2

219 x 12 y 1 1

3

(b)

221

12 x 9 y 1 13

(c)

2

2

1x

y 121

12 9

(d) 2

213 x 4 y 1 1

2

35. If 1p and 2p are the perpendiculars from the origin on the straight lines

x sec ycosec 2a and x cos ysin a cos 2 , then

(a) 2 2 2

1 24p p a (b) 2 2 2

1 2p 4p a

(c) 2 2 2

1 2p p 4a (d) 2 2 2

1 2p p a

36. If c is the centre and A, B are two points on the conic 2 24x 9y 8x 36y 4 0 such

that ACB ,2

then

2 2CA CB is equal to

(a) 13

36 (b)

36

13

(c) 16

33 (d)

33

16

37. A point moves such that the sum of the squares of its distances from the two sides of

length a of a rectangle is twice the sum of the squares of its distances from the other two

sides of length b. the locus of the point can be

(a) a circle (b) an ellipse

(c) a hyperbola (d) a pair of lines

38. If the tangent at the point 1 1P x , y to the parabola 2y 4ax meets the parabola

2y 4a x b at Q and R, then the mid–point of QR is

(a) 1 1x b, y b (b) 1 1x b, y b

(c) 1 1x , y (d) 1 1x b, y

39. If , are the eccentric angels of the extremities of a focal chord of an ellipse, then the

eccentricity of the ellipse is

(a)

cos cos

cos

(b)

sin sin

sin


(c)

cos cos

cos

(d)

sin sin

sin

40. PQ and RS are two perpendicular chords of t rectangular hyperbola xy = c2. If O is the

centre of the hyperbola, then the product of the slopes of OP, OQ, OR and OS is equal to

(a) –1 (b) 1

(c) 2 (d) 4

41. Let f be the focus of the parabola. From the end point (P) of focal chord PF

perpendicular PM is drawn to directix. From P a line is drawn through the mid–point (R)

of FM, then the angle between PR and FM is

(a) 45 (b) 60


42. A normal drawn to parabola 2y 4ax meet the curve again at Q such that angle subtend

by PQ at vertex is 90 then coordinate of P can be

(a) 8a, 4 2a (b) 8a,4a

(c) 2a, 2 2a (d) none of these

43. If the focus of parabola (y–k)2=4(x–h) always lies between the line x + y = 1 and

x + y = 3 then

(a) 0 h k 2 (b) 0 h k 1

(c) 1 h k 2 (d) 1 h k 3

44. If xy = m2–4 be a rectangular hyperbola whose branches lies only in the 2

nd and 4

th

quadrant then

(a) m 2 (b) m 2

(c) m 2 (d) not possible

45. A tangent to the ellipse 2 2x y

125 16

at any point P meet the line x = 0 at a point Q. Let

R b the image of Q in the line y =x, then circle whose extremities of a diameter are Q

and R passes through a fixed point. The fixed point is

(A) (3,0) (B) (5,0)

(C) (0,0) (D) (4,0)

46. Number of points on the ellipse 2 2x y

150 20

from which pair of perpendicular tangents

are drawn to the ellipse 2 2x y

116 9

is

(A) 0 (B) 2

(C) 1 (D) 4

47. An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using

one focus and centre, a circle is drawn that is tangent to the ellipse, with no part of the

circle being outside the ellipse. The radius of the circle is :

(A) 2 (B) 3

(C) 3 (D) 4

48. A circle has the same centre as an ellipse and passes through the foci F1 and F2 of the

ellipse, such that the two curves intersect in 4 points. Let P be any one of their point

of intersection. If the major axis of the ellipse is 17 and the area of the triangle PF1F2

is 30, then the distance between the foci is

(A) 11 (B) 12

(C) 13 (D) 15


49. Any ordinate MP of an ellipse 2 2x y

125 9

meets the auxiliary circle in Q, then locus

of point of intersection of normals at P and Q to the respective curves, is

(A) 11 (B) 12

(C) 13 (D) 15

50. Number of distinct normal lines that can be drawn to ellipse 2 2x y

1169 25

from the

point P(0,6) is

(A) one (B) two

(C) three (D) four

51. If PQ is focal chord of ellipse 2 2x y

125 16

which passes through S (3,0) and PS = 2

then length of chord PQ is

(A) 8 (B) 6

(C) 10 (D) 4

52. If P is a moving point in the xy-plane is such a way that perimeter of triangle PQR is

16 {where Q (3, 5) , R (7,3 5 )} then maximum area of triangle PQR is

(A) 6 sq. unit (B) 12 sq. unit

(C) 18 sq. unit (D) 9 sq. unit

53. If f(x) is a decreasing function then the set of values of ‘k’, for which the major axis

of the ellipse

2 2

2

x y1

f k 11f k 2k 5

is the x-axis, is

(A) k 2,3 (B) k 3,2

(C) k , 3 2, (D) k , 2 3,

54. The equation to the locus of the middle point of the portion of the tangent to the

ellipse 2 2x y

116 9

included between the co-ordinate axes is the curve

(A) 9x2

+ 16y2 = 4 x

2y

2 (B) 16x

2 + 9y

2 = 4 x

2y

2

(C) 3x2

+ 4y2 = 4 x

2y

2 (D) 9x

2 + 16y

2 = x

2y

2

55. From a point P(1,2) pair of tangent’s are drawn to a hyperbola ‘H’ in which one

tangent to each are of hyperbola. H are 3x y 5 0 and 3x y 1 0 3x y 0

then eccentricity of H is

(A) 2 (B) 2

3

(C) 2 (D) 3

56. If a variable lines has its intercepts on the coordinates axes e, e where e e

,2 2

are the

eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches

the circle 2 2 2x y r , where r =

(A) 1 (B) 2

(C) 3 (D) can not be decided

57. If angle between asymptote’s of hyperbola 2 2

2 2

x y1

a b is 120 and product of

perpendiculars drawn from foci upon its any tangent is 9, then locus of point of

intersection of perpendicular tangent of the hyperbola can be

(A) 2 2x y 6 (B) 2 2x y 9


(C) 2 2x y 3 (D) 2 2x y 18

58. C be a curve which is locus of point of intersection of lines x = 2 + m and my=4–m.

A circle 2 2

s x 2 y 1 25 intersects the curve C at four points, P, Q, R and S.

If O is centre of the curve C, then OP2 + OQ

2 + OS

2 is

(A) 50 (B) 100

(C) 25 (D) 25/2

59. The combined equation of the asymptotes of the hyperbola 2 22x 5xy 2y 4x 5y 0 is

(A) 2 22x 5xy 2y 4x 5y 2 0 (B) 2 22x 5xy 2y 4x 5y 2 0

(C) 2 22x 5xy 2y 0 (D) none of these

60. If 3 then the chord joining the points and for the hyperbola 2 2

2 2

x y1

a b

passes through

(A) focus (B) centre

(C) one of the end points of the transverse axis

(D) one of the end points of the conjugates axis

61. For a given non-zero value of m each of the lines x y

ma b and

x ym

a b meets the

hyperbola 2 2

2 2

x y

a b = 1 at a point. Sum of the ordinates of these points, is

(A) 2a 1 m

m

(B)

2b 1 m

m

(C) 0 (D) a b

2m

62. The equation of the transverse axis of the hyperbola (x-3)2 + (y+1)

2 = (4x + 3y)

2 is

(A) x + 3y = 0 (B) 4x + 3y = 9

(C) 3x – 4y = 13 (D) 4x + 3y = 0

63. For which of the hyperbola, we can have more than one pair of perpendicular

tangents ?

(A) 2 2x y

14 9 (B)

2 2x y1

4 9

(C) 2 2x y 4 (D) xy 4

64. From point (2,2) tangents are drawn to the hyperbola 2 2x y

116 9

then point of contact

lie in

(A) I and II quadrants (B) I and IV quadrants

(C) I and III quadrants (D) III and IV quadrants

65. A circle is described whose centre is the vertex and whose diameter is three-quarters

of the latus rectum of the parabola 2y 4ax. If PQ is the common chord of the circle

and the parabola and L1L2 is the latus rectum, then the area of the trapezium PL1L2Q

is

(A) 23 2a (B) 22 2a

(C) 24a (D) 22 2a

2

66. From the point (15,12) three normals are drawn to the parabola 2y 4x, then centroid

of triangle formed by three-co-normal points is


(A) 16

,03

(B) 4,0

(C) 26

,03

(D) 6,0

67. Through the vertex O of the parabola y2 =4ax two chords OP and OQ are drawn and

the circles on OP and OQ as diameter intersect in R. If 1 2, & are the angle made

with the axis by the tangents at P and Q on the parabola and by OR then

cot 1 2cot is equal to

(A) 2tan (B) 2tan

(C) 0 (D) 2cot

68. A ray of light travels along a line y = 4 and strikes the surface of a curve 2y 4 x y

then equation of the line along reflected ray travel is

(A) x = 0 (B) x = 2

(C) x + y = 4 (D) 2x+y = 4

69. If P be a point on the parabola 2y 3 2x 3 and M is the foot of perpendicular drawn

from P on the directix of the parabola, then length of the each side of an equilateral

triangle SMP, where S is focus of the parabola, is

(A) 2 (B) 4

(C) 6 (D) 8

70. If the locus of middle point of contact of tangent drawn to the parabola 2y 8x and

foot of perpendicular drawn from its focus to the tangent is a conic then length of

latusrecturm of this conic is

(A) 9/4 (B) 9

(C) 18 (D) 9/2

71. Normals at three points P, Q, R at the parabola 2y 4ax meet in a point A and S be its

focus, if 2

SP . SQ . SR SA , then is equal to

(A) a3 (B) a

2

(C) a (D) 1

72. If the chord of contact of tangents from a point P to the parabola 2y 4ax touches the

parabola 2x 4by , the locus of P is

(A) circle (B) parabola

(C) ellipse (D) hyperbola

73. Minimum area of circle which touches the parabola’s 2y x 1 and 2y x 1 is

(A) 9

sq.unit16

(B)

9sq.unit

32

(C) 9

sq.unit8

(D)

9sq.unit

4

74. Let P and Q be points (4,-4) and (9,6) of the parabola 2y 4a x b . Let R be a point

on the arc of the parabola between P and Q. Then the area of PRQ is largest when

(A) PRQ 90 (B) then point R is (4,4)

(C) the point R is 1

,14

(D) none of these

ONE OR MORE THAN ONE CORRECT


75. If P is a point of the ellipse 2 2

2 2

x y1

a b , whose foci are S and S. Let PSS and

PS S , then

(A) PS PS 2a, if a > b

(B) PS PS 2b, if a < b

(C) 1 e

tan tan2 2 1 e

(D) 2 2

2 2

2

a btan tan a a b

2 2 b

when a > b

76. If the chord through the points whose eccentric angles are and on the ellipse, 2 2

2 2

x x1

a b passes through a focus, then the value of tan / 2 tan / 2 is :

(A) e 1

e 1

(B)

e 1

e 1

(C) 1 e

1 e

(D)

1 e

1 e

77. The equation 2 23x 4y 18x 16y 43 c

(A) cannot represent a real pair of straight lines for any value of c

(B) represents an ellipse , if c > 0

(C) represents empty set, if c < 0

(D) a point, if c = 0

78. If foci of 2 2

2 2

x y1

a b concide with the foci of

2 2x y1

25 9 and eccentricity of the

hyperbola is 2, then

(A) 2 2a b 16

(B) there is no director circle to the hyperbola

(C) centre of the director circle is (0,0)

(D) length of latus rectum of the hyperbola = 12

79. If (5,12) and (24,7) are the foci of a conic passing through the origin then the

eccentricity of conic is

(A) 386

12 (B)

386

13

(C) 386

25 (D)

386

38

80. For the hyperbola 2 29x 16y 18x 32y 151 0

(A) One of the directrix is 21

x5

(B) length of latus rectum = 9

2

(C) Focii are (6,1) and (-4,1) (D) eccentricity is 5

4

Subjective Type 81. Two parabolas have a common axis and concavities in opposite directions; if any line

parallel to the common axis meet the parabolas in P and P, prove that the locus of the

middle point of PP is another parabola, provided that the latus recta of the given

parabolas are unequal.


82. The normal at any point P meets the axis in G and the tangent at the vertex in G, if A be

the vertex and the rectangle AGQG be completed, prove that the equation to the locus of

Q is x3 = 2ax

2 + ay

2

83. If a normal to a parabola make an angle of with the axis, show that it will cut the curve

again at angle 1 1tan tan

2

84. If PQ be a normal chord of the parabola and if S be the focus, prove that the locus of the

centroid of the triangle SPQ is the curve

2 4 436ay 3x 5a 81y 128a

85. If from the vertex of a parabola a pair of chord be drawn at right angles to one another

and with these chords as adjacent sides a rectangle be made, prove that the locus of the

further angle of the rectangle is the parabola y2=4a(x–8a)

86. Prove that the orthocentres of the triangles formed by three tangents and the

corresponding three normals to a parabola are equidistant from the axis.

87. Circles are drawn through the vertex of the parabola to cut the parabola at the other point

of intersection.

Prove that the locus of the centres of the circles is the curve

22 2 22y 2y x 12ax ax 3x 4a

88. Through the vertex A of the parabola y2-=4ax two chords AP and AQ are drawn, and the

circles on AP and AQ as diameters intersect in R. Prove that, if 1 2, and be the

angles made with the axis by the tangents at P and Q and by AR, then

1 2cot cot 2 tan 0

89. If the normals at the three points P,Q and R meet in a point and if PP, QQ and RR be

chords parallel to QR, RP and PQ respectively, prove that the nromals at P, Q and R

and also meet in a point

90. The sides of a triangle touch a parabola and two of its angular point lie on another

parabola with its axis in the same direction; prove that the locus of the third angular

points in another parabola.

91. The tangent at any point P of a circle meets the tangent at a fixed point a in T, and T is

joined to B, the other end of the diameters through A; prove that the locus of the

intersection of AP and BT is an ellipse whose eccentricity is 1

2

92. Find the locus of intersection of the two straight lines tx y

t 0a b and

x ty1 0

a b .

Prove also that they meet at the point whose eccentric angle is 2 tan–1

t.

93. If the straight line y=mx+c meet the ellipse, prove that the equation to the circle,

described on the line joining the points of intersection as diameter, is

2 2 2 2 2 2 2 2 2 2 2 2 2a m b x y 2ma cx 2b cy c a b a b 1 m 0 .

94. Prove that the sum of the eccentric angles of the extremities of a chord, which is drawn

in a given direction, is constant and equal to twice the eccentric angle of the point at

which the tangent is parallel to the given direction.

95. The eccentric angles of two point P and Q on the ellipse are 1 and 2 ; prove that the

area of the parallelogram formed by the tangents at the ends of the diameters. Through P

and q is 4abcosec 1 2 and hence that it is least when P and q are at the end of

conjugate diameters.


96. In both an ellipse and a hyperbola, prove that the focal distance of any point and the

perpendicular from the centre upon the tangent as it meet on a circle whose centre is the

focus and whose radius is the semi–transverse axis.

97. Given the base of a triangle and the ratio of the tangent of half the base angles, prove that

the vertex moves on a hyperbola whose foci are extremities of the base.

98. A straight line is drawn parallel to the conjugate axis of a hyperbola to meet it and the

conjugate hyperbola in the point s P and q; show that the tangents at P and Q meet on the

curve 4 2 2 2

2 2 2

y y x 4x

b b a a

99. Find the equation to the hyperbola, whose asymptotes are straight lines x+2y+3=0 and

3x+4y+5=0, and whish passes through the point (1,–1).

Write down also the equation to the conjugate hyperbola.

100. C is the centre of the hyperbola 2 2

2 2

x y1

a b and the tangent at any point P meets the

asymptote in the point q and r. Prove that the equation to the locus of the centre of the

circle circumscribing the triangle CQR is 2

2 2 2 2 2 24 a x b y a b

101. Let V be the vertex and L be the latusrectum of the parabola 2x 2y 4x 4. then the

equation of the parabola whose vertex is at V, latusrectum is L/2 and axis is

perpendicular to the axis of the given parabola.

(A) 2y x 2 (B) 2y x 4

(C) 2y 2 x (D) 2y 4 x

102. If equation of tangent at P, Q and vertex A of a parabola are 3x 4y 7 0 ,

2x + 3y-10=0 and x – y = 0 respectively, then

(A) focus is (4,5) (B) length of latus rectum is 2 2

(C) axis is x y 9 0 (D) vertex is 9 9

,2 2

103. If A and B are points on the parabola 2y 4ax with vertex O such that OA

perpendicular to OB and having length, r1 and r2 respectively, then the value of 4/3 4/3

1 2

2/3 2/3

1 2

r r

r r is

(A) 216a (B) 2a

(C) 4a (D) none of these

104. Let P, Q and R are three co-normal points on the parabola 2y 4ax. then the correct

statement(s) is / are

(A) algebraic sum of the slopes of the normals at P, Q and R vanishes

(B) algebraic sum of the ordinates of the points P, Q and R vanishes

(C) centroid of the triangle PQR lies on the axis of the parabola

(D) circle circumscribing the triangle PQR passes through the vertex of the

parabola.

105. The locus of the mid point of the focal radii of a variable point moving on the

parabola , 2y 4ax is a parabola whose

(A) latus rectum is half the latus rectum of the original parabola

(B) vertex is (a/2.0)

(C) directix is y-axis

(D) Focus has the co-ordinates (a,0)

JEE Advanced Maths Assignment - NARAYANA IIT ...// JEE–Advanced Maths – Assignment Only One...

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