Chapter 8.1-8.3 Review
Find the vertex, focus, directrix, and focal width of the parabola.
1) y 2 = 16x
2) (x - 1)2 = 16(y + 6)
1)
2)
Find the standard form of the equation of the parabola.
3) Focus at (4, -9), directrix x = 2
3)
Graph the parabola.
4) (x + 3)2 = 2(y - 5)
4)
y
10
10 x
-10
-10
Find the vertex, the focus, and the directrix of the parabola.
5) x2 + 8x - 4y + 36 = 0
Find the center, vertices, and foci of the ellipse with the given equation.
2
2
6) (x + 5) + (y - 3) = 1
225
81
Graph the ellipse.
2
2
7) x + y = 1
16
49
5)
6)
7)
y
x
Find an equation in standard form for the ellipse that satisfies the given conditions.
8) The vertical major axis is of length 18, and the minor axis is of length 10.
1
8)
Find the eccentricity of the ellipse.
9) x2 + 3y 2 = 15
9)
Find the vertices,foci, and asymptotes of the hyperbola.
2
2
10) x - y = 1
9
72
10)
Graph the hyperbola.
2
2
11) y - x = 1
64
25
11)
y
10
5
-10
-5
5
10 x
-5
-10
Find the eccentricity of the hyperbola.
12) x2 - 2y 2 = 6
12)
Find an equation in standard form for the hyperbola that satisfies the given conditions.
13) Center (2, -3), focus (7, -3), vertex (5, -3)
13)
2
Answer Key
Testname: CHPT8REVIEW
1) Vertex: (0, 0); Focus: (4, 0); Directrix: x = -4; Focal width: 16
2) Vertex: (1, -6); Focus: (1, -2); Directrix: y = -10; Focal width: 16
3) (y + 9)2 = 4(x - 3)
4)
y
10
10 x
-10
-10
5) Vertex: -4, 5 ; Focus: (-4, 6); Directrix: y = 4
6) Center: (-5, 3); Vertices: (-20, 3), (10, 3); Foci: (-17, 3), (7, 3)
7)
y
x
2
2
8) x + y = 1
25
81
9) i
2
3
10) Vertices: (± 3, 0); Foci: (± 9, 0)
11)
y
10
5
-10
-5
5
10 x
-5
-10
3
Answer Key
Testname: CHPT8REVIEW
12)
6
2
2
2
13) (x - 2) - (y + 3) = 1
9
16
4