Anlytical Geometry

STD:XII ANALYTICAL GEOMETRY MARKS:80

SIX MARKS:1. If a parabolic reflector is 20cm in diameter and 5cm deep, find the distance of the

focus from the centre of the reflector.

2. The focus of a parabolic mirror is at a distance of 8cm from its centre (vertex). If the mirror is 25cm deep, find the diameter of the mirror.

3. Find the equation of the ellipse if (each) the centre is (3, - 4), one of the foci is

(3+√3 ,−4 ) and e =

√32 .

4. Find the equation of the ellipse if (each) the centre is (3, - 1), one of the foci is (6 – 1) and passing through the point (8, - 1).

5. Find the vertex, foci , L.R, lenth of the L.R, directrices of parabola (x-4)2=4(y+2)

TEN MARKS:6. The girder of a railway bridge is in the parabolic form with span 100ft and the highest point on the arch is 10ft above the bridge. Find the height of the bridge at 10ft to the left or right from the mid point of the bridge.

7. on lighting a rocket cracker it gets projected in a paraboloic path and reaches a maximum height

of 4mts. when it is 6mts. away from the point of projection.Finally it reaches the ground 12mts. away from the starting point. Find the angle of projection.

8. Assume that water issuing from the end of a horizontal pipe, 7.5m above the ground, describes a

parabolic path, the vertex of the parabolic is at the end of the pipe. At a position 2.5m below the

line of the pipe, the flow of water has curved outward 3m beyond the vertical line through the end

of the pipe. How far beyond this vertical line will the water strike the ground?

9. A cable of a suspension bridge is in the form of a parabola whose span is 40mts. The road way is 5mts. below the lowest point of the cable. If an extra support is provided across the cable 30 mts. above the ground level, find the length of the support if the height of the pillars are 55mts.

10. Find the vertex, foci , L.R, lenth of the L.R, directrices of parabola y2+8x-6y+1=0