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Pre-Calculus
Unit 12 Test Review
1.
Name: ____________________________
Matching: Put the letter in front of the correct Shape.
_____ a. Parabola opening left
A.
(x – h)2 + (y – k)2 = r 2
_____ b. Parabola opening down
B.
y = a(x – h)2 + k; a < 0
_____ c. Parabola opening right
C.
y = a(x – h)2 + k; a > 0
_____ d. Parabola opening up
D.
x = a (y – k)2 + h, a < 0
_____ e. Vertical Ellipse
E.
x = a (y – k)2 + h, a > 0
_____ f. Vertical Hyperbola
F.
_____ g. Horizontal Hyperbola
G.
_____ h. Horizontal Ellipse
H.
I.
( x  h) 2
a2
( x  h) 2
b2
( x  h) 2
a2
( y  k )2
a2
( y  k)2
1
b2
( y  k)2

1
a2
( y  k)2

1
b2
( x  h) 2

1
b2

Give the a, b, c relationship for
i. Ellipse
j. Hyperbola
k. Give the formula for the distance from the vertex to the focus for a parabola ________
2. What is the difference between the values of “c” for an ellipse and a hyperbola?
3. How can you tell the difference between the conic sections by looking at the equation?
4. What is eccentricity? How do you find its value??
Write the equation for the following graphs in standard form:
5.
6.






Focus 













Equation: _____________________
Equation: _____________________
7.












Equation: _____________________
Write the equation for each conic section described below. Draw a sketch above if needed!
8.
Ellipse with foci at (4, 0) and (-4, 0). The endpoints of the minor axis are at (0, 2) and (0, -2).
Equation: ______________________________
9.
Hyperbola with vertices at (2, 2) and (2, -4) and one focus point at (2, 4)
Equation: ______________________________
10. Given x = 
1
2
 y  4   3 , find the following; and graph
12
Vertex Point: ______________
Focus Point: _______________
AOS: ____________________
Opening Direction: __________
Directrix Equation: ____________________
End Points for Latus Rectum: ______________________
x2 y 2
11. Given the equation 
 1 find the following and graph
49 25
Horizontal or Vertical
Center Point: _____________
Length Transverse Axis: ___________
Equation of Asymptotes: _________________
Vertex Points: V1: _____________, V2: _____________
Foci: F1: ___________, F2: ____________
12. Given the equation,
( x  2) 2 ( y  1) 2

 1, find the following and graph
16
36
Horizontal or Vertical
Center Point: __________________
Major Axis Length: ______________
Minor Axis Length: ______________
Eccentricity: ___________________
Foci: F1: ___________, F2: ____________
Complete the square on each of the following equations to get standard format of a conic section
13. 2 x 2  3 y 2  8x  18 y  13  0
15.
5 y  2 x2  8x  10  0
14. y 2  4 x 2  8 y  16 x  12  0
16. 12 x  3 y 2  18 y  3
Applications of conic sections:
17. A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the
receiver, which is placed at the focus, if the dish is 10 feet across at it opening and 5 feet deep.
18. The opening of a tunnel that goes through the Rocky Mountains is in the shape of a semielliptical arch. The arch is 60 feet wide and 40 feet high. Write an equation that models the arch.
Also find the height of the arch 10 feet right of centerline.
19. A new highway is under construction. The road will model a parabolic from center to outside to
provide for proper drainage. If the road is 32 feet across and is 0.7 feet high at the center, write an
equation that models the road. Also find the distance from center of the road where the drop is 0.2
feet.
0.7 feet
32 feet
20. Some comets have elliptical orbits. Find the equation of the path of Panther’s Comet in
astronomical units by letting the sun (one focus) be at the origin and the other focus on the positive xaxis. The length of the major axis of the orbit of Panther’s Comet is approximately 20 astronomical
units (AU) and the length of the minor axis is 12 astronomical units (AU).
21. Halley ’s Comet has an elliptical orbit, with the sun at one focus. The eccentricity of the orbit is
approximately 0.967. The length of the major axis of the orbit is approximately 35.88 astronomical
units. (An astronomical unit is about 93 million miles.)
a. Find an equation of the orbit. Place the center of the orbit at the origin, and place the
major axis on the x-axis.
b. Find the length of the Aphelion and Perihelion.