Pre-Calculus
Conic Sections Review Sheet
Name: _____________________________________
For numbers 1 – 3, refer to the ellipse represented by
1.
 x  1
16
2

 y  2
9
2
 1.
Find the coordinates of the center.
b) (–1, –2)
a) (1, 2)
2.
c) (–1, 2)
d) (–2, 1)
e) (1, –2)
d) (1, 4), (1, –8)
e) (–4, –2) , (6, –2)
Find the coordinates of the foci.

a) 1  7,  2
3.

b) (5, –2) , (–3, –2)

c) 1,  2  7

Find the coordinates of the vertices and co-vertices.
a) (1, 2), (1, –6), (4, –2), (–2, –2)
b) (5, –2), (–3, –2), (1, 1), (1, –5)
c) (4, 2), (–2, 2), (1, 1), (1, –5)
d) (5, –2), (–3, –2), (1, 2), (1, –6)
e) Ellipses don’t have co-vertices
Use the discriminant to identify the conic section 9y2 + 4x2 – 108y + 24x = –144.
5.
a) parabola
7.
b) hyperbola
c) ellipse
d) circle
e) line
Find the equation of the vertical parabola with the vertex at the origin and the distance from the vertex to the focus is 2 units.
a) y2 = 4x
b) x2 = 4y
c) y2 = 8x
For numbers 8 & 9, refer to the hyperbola represented by
8.
d) x2 = 8y
e) y2 = 16x
y2 x2

 1.
4
2
Write the equations of the asymptotes.
1
b) y =  x
2
a) y = ± 2x
9.
c) y =  2x
d) y = 
2
x
2
e) None of these


e) None of these
Find the coordinates of the foci.

a) 0,  2


b) 0,  6


c)  2, 0

d)  6, 0
10. Write the standard form of the equation of the hyperbola for which the transverse axis is 4 units long and vertical and the
conjugate axis is 3 units long.
a)
d)
 x  1
2

2.25
 x  1
4
2

 y  4
2
4
 y  4
1
b)
1
e)
2
2.25
 y  4
2
2.25
 y  4

2
4

 x  1
2
4
 x  1
1
c)
 y  4
2.25
2

 x  1
4
2
1
2
2.25
1
12. Write the standard form of the equation of the parabola with directrix at x = –1 and with focus at (5, –2).
a) (y + 2)2 = 12(x + 2)
b) (y + 2)2 = 12(x – 2)
c) 12(x + 2)2 = y – 2
d) (y + 2)2 = –12(x + 2)
e) (x + 2)2 = 12(y + 2)
13. Identify the graph of the equation 16x2 – 24xy + 9y2 – 30x – 40y = 0, using the discriminant.
a) hyperbola
b) ellipse
c) parabola
d) circle
e) line
14. Which graph represents a curve with parametric equations x = t – 4 and y = t2 over the interval – 2 ≤ t ≤ 2?
a)
b)
c)
15. Identify the conic that may have an eccentricity of
a) circle
b) ellipse
16. Write the standard form. Identify the conic.
a) circle
b) ellipse
d)
e) None of these
d) parabola
e) line
d) parabola
e) line
d) (1, 0)
e) (4, 0)
d) y = 7
e) y = 28
4
.
3
c) hyperbola
x2 + 4y2 – 6x – 7 = 0
c) hyperbola
17. What is the focus of the parabola with equation 2y2 = 8x?
a) (–1, 0)
b) (0, 1)
c) (0, 2)
18. What is the directrix of the parabola with equation x2 = –28y?
a) x = 7
b) x = 28
c) y = –7
19. Which equation is graphed?
a)
x2 y 2

1
16 9
b)
x2 y 2

1
16 9
c)
y 2 x2
 1
16 9
d)
y 2 x2
 1
16 9
e) None of these
20. What are the foci of the ellipse 8x2 + 12y2 = 96?
a) (–3, 0), (3, 0)
b) (–2, 0), (0, 2)
d) (0, –3), (0, 3)
c) (–2, 0), (2, 0)
e) (0, –2), (0, 2)
21. What is the equation of the ellipse with center at (0, 0), vertex at (5, 0), and focus at (2, 0)?
a)
x2 y 2

1
25 21
b)
x2 y 2

1
25 9
c)
x2 y 2

1
9 25
d)
x2 y 2

1
5 3
e)
22. Which of the following is an equation of the ellipse with foci at (2, 4) and (–6, 4) and
a)
d)
 x  4
2

20
 x  2
20
 y  2
2

2
1
36
 y  4
36
b)
2
1
e)
 x  4
2
36
 x  2
36

2

 y  2
 y  4
20
1
b) 0.837
c)
b) 1.27
36
2

 y  4
20
2
1
1
 x  8
2
14

 y  3
2
57
c) 0.426
24. Determine the eccentricity of the hyperbola that has an equation of
a) 1.52
 x  2
2
23. Determine the eccentricity of the ellipse that has an equation of
a) 0.5
vertices at (–8, 4) and (4, 4)?
2
20
x2 y 2

1
21 25
 1.
d) 0.511
 y  1
10
c) 1.06
2

 x  6
13
e) 0.869
2
 1.
d) 1.33
e) 2.03
d) right
e) none
25. Determine the orientation of the parabola: focus (0, 4), directrix y = 1
a) up
b) down
c) left