Trig/Pre-Cal Unit 4B Review
Conic Sections
Find the standard form of the equation of the hyperbola.
Complete the square and write the equation in standard
form. Then give the center and radius of the circle.
1) x2 + y2 + 14x - 14y = -73
12)
Find the standard form equation of the cirlce whose diameter
endpoints are given.
2) (9, 1) and (5, 9)
Graph the equation.
3) x2 + y2 + 8x + 2y - 8 = 0
Graph the ellipse. Find the foci.
(x + 2)2 (y - 1)2
4)
+
=1
4
9
5) 4(x - 1)2 + 16(y + 1)2 = 64
Find the standard form of the equation of the ellipse and
give the location of its foci.
6) Center at (-2, 3)
Find the standard form of the equation of the hyperbola
satisfying the given conditions.
13) Center: (6, 5); Focus: (3, 5); Vertex: (5, 5)
14) Endpoints of transverse axis: (0, -10), (0, 10);
asymptote: y =
5
x
8
Convert the equation to the standard form for a hyperbola
by completing the square on x and y.
15) 4x 2 - 25y2 - 8x + 50y - 121 = 0
Graph the parabola with the given equation. Find the
vertex, focus, and directrix
16) (y + 2)2 = -8(x + 1)
17) (x - 1)2 = -8(y + 2)
Find the standard form of the equation of the ellipse
satisfying the given conditions.
7) Endpoints of major axis: (-2, -1) and (-2, 7);
endpoints of minor axis: (-4, 3) and (0, 3);
Find the standard form of the equation of the parabola
using the information given.
18) Focus: (-3, -1); Directrix: x = 7
19) Vertex: (4, -8); Focus: (4, -7)
8) Major axis horizontal with length 12; length of
Convert the equation to the standard form for a parabola
by completing the square on x or y as appropriate.
20) y2 - 4y - 2x - 2 = 0
minor axis = 6; center (0, 0)
Convert the equation to the standard form for an ellipse
by completing the square on x and y.
9) 36x 2 + 9y2 - 216x + 36y + 36 = 0
21) x2 - 6x - 6y - 21 = 0
Use the center, vertices, and asymptotes to graph the
hyperbola. Find the foci.
(x - 2)2 (y + 1)2
10)
=1
4
9
Identify the equation without completing the square.
22) 2x 2 - 2y2 + 5x + 4y + 2 = 0
23) 3x 2 - 3x + y + 1 = 0
24) 3x 2 + 4y2 + 3x - 2 = 0
11) (y + 2)2 - 4(x - 3)2 = 4
25) 5x 2 - 6y2 + 2x - 3y - 5 = 0
1
Answer Key
Testname: UNIT 4B REVIEW
1) (x + 7)2 + (y - 7)2 = 25
(-7, 7), r = 5
2) (7, 5)
3)
9)
(x - 3)2 (y + 2)2
+
=1
9
36
16)
10)
17)
4)
11)
18) (y + 1)2 = -20(x - 2)
19) (x - 4)2 = 4(y + 8)
5)
12)
(y + 1)2 (x + 1)2
=1
9
4
(y - 5)2
=1
13) (x - 6)2 8
6)
14)
y2
x2
=1
100 256
15)
(x - 1)2 (y - 1)2
=1
25
4
(x + 2)2 (y - 3)2
+
=1
36
9
foci at (-2 + 3 3, 3) and (-2
- 3 3, 3)
(x + 2)2 (y - 3)2
+
=1
7)
4
16
8)
x2 y2
+
=1
36
9
2
20) (y - 2)2 = 2(x + 3)
21) (x - 3)2 = 6(y + 5)
22) hyperbola
23) parabola
24) ellipse
25) hyperbola