Conics Test

Last chance to SHINE!!

Unit 12 Conics Test

• Conic Graphing: 39 pts• Completing the Square: 7 pts• Writing Equations: 14 pts• Conic Applications: 40 pts

Study Hints• Know equations cold• Know what determines orientation• DO NOT get Vertex or CP wrong!!!• Know what 1/4a does. What |1/a| does.• Know what a, b, and c do for an ellipse & hyperbola• Know how to calculate eccentricty• Know how to complete the square• Know satellite dish applications• Know Quad Regression applications• Know perihelion & aphelion

2 2( 3) ( 1) 136 9x y

:CPMajor Axis Length:

Minor Axis Length: Eccentricity:

FP 1: FP 2:

635.2

abc

( 3,1)126

0.867( 8.2,1) (2.2,1)

2 2( 1) ( 4) 116 25y x

:CPTransverse Axis Length:

Conjugate Axis Length: Asymptote Slope:

FP 1: FP 2:

456.4

abc

(4, 1)8

1045

(4,5.4) (4, 7.4)

2 22 4 8 24 44 0x y x y 2 2(2 8 ) ( 4 24 ) 44x x y y

2 22( 4 ___) 4( 6 __) 44x x y y 2 22( 4 4) 4( 6 9) 44 8 36x x y y

2 22( 2) 4( 3) 16x y 2 2( 2) ( 3) 1

8 4x y

Given Focus at (-3,7)Directrix is x = 5Write the equation??

2( )x a y k h

1 44 116 1

116

aa

a

21 7 116

( )x y

A satellite dish is shaped like a parabolic. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located (the focus). If the dish is 10 feet across at its opening and is 4 feet deep at its center, at what position should the receiver be placed?

Satellite Continued

10’

4’

Since opening is 10’, then either side is 5’ (-5, 4) and (5, 4)

y = a(x – h)2 + k; but (h, k) = (0, 0)

y = ax2

(5, 4) is an ordered pair on the parabola

4 = a 52

4 = 25a

a = 4/25

1 144 425

1 25 1.5616 1625

pa

units fromVertex

The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway

between the towers, what is the height of the cable at a point 150 feet from a tower?

(0,80)(300,0)(600,80)

2.00089 .533 80y x x

Data Table(150,20)20 feet

Mars has an elliptical orbit with the sun as one focus and an eccentricity value of .0934.If its major axis has a length of 456 Gm, then write an equation for the orbit (center point at origin) and find the perihelion and aphelion from the sun.

2 456, 228a so a

, .0934 21.30228

c ce so or ca

2 2 2

2 2 2228 21.30 51530.31

b a c

b

2 2

151,984 51530.31x y

249.30Aphelion a c Gm

206.70Perihelion a c Gm