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Hyperbolas
Find the vertices and foci of the hyperbola.
- x2 4 - y2 60 = 1
A) Vertices: (0, ± 8); Foci: (0, ± 2) B) Vertices: (± 2, 0); Foci: (± 8, 0) C) Vertices: (0, ± 2); Foci: (0, ±8) D) Vertices: (± 8, 0); Foci: (± 2, 0)
- (x^144 -^ 5)2 - (y^ - 81 4)2 = 1
A) Vertices: (14, 4), (-4, 4); Foci: (-4, 4), (14, 4) B) Vertices: (4, 17), (4, - 7); Foci: (4, - 10), (4, 20) C) Vertices: (4, 14), (4, - 4); Foci: (4, - 4), (4, 14) D) Vertices: (17, 4), (-7, 4); Foci: (-10, 4), (20, 4)
- (y^ + 64 4)2 - (x^ + 36 2)2 = 1
A) Vertices: (2, - 2), (-10, - 2); Foci: (-10, - 2), (2, - 2) B) Vertices: (-2, 4), (-2, - 12); Foci: (-2, 6), (-2, - 14) C) Vertices: (4, - 2), (-12, - 2); Foci: (6, - 2), (-14, - 2) D) Vertices: (-2, 2), (-2, - 10); Foci: (-2, - 10), (-2, 2)
Match the given graph with its equation.
-8 -6 -4 -2 2 4 6 8 x
y 6 4 2
-8 -6 -4 -2 2 4 6 8 x
y 6 4 2
A) x 9
= 1 B) x 9
= 1 C) x 25
= 1 D) y 9
-8 -6 -4 -2 2 4 6 8 x
y 6 4 2
-8 -6 -4 -2 2 4 6 8 x
y 6 4 2
A) y 9
= 1 B) y 25
= 1 C) x 9
= 1 D) y 9
-8 -6 -4 -2 2 4 6 8 x
y 6 4 2
-8 -6 -4 -2 2 4 6 8 x
y 6 4 2
A) 4y2^ - 25x2^ = 100 B) 25x2^ - 4y2^ = 100 C) 25x2^ + 4y2^ = 100 D) 4x2^ - 25y2^ = 100
-8 -6 -4 -2 2 4 6 8 x
y 2
-8 -6 -4 -2 2 4 6 8 x
y 2
A) (x^ -^ 1) 16
= 1 B) (x^ +^ 3) 16
C) (y^ + 4 3)2- (x^ - 16 1)2 = 1 D) (x^ - 4 1)2 - (y^ + 16 3)2 = 1
- (x^ +^ 2) 49
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
- (y^ +^ 1) 4
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
- 25y2^ - 36x2^ = 900
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
- 16x2^ - 9y2^ = 144
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
Find an equation in standard form for the hyperbola that satisfies the given conditions.
- Vertices at (±2, 0), foci at (±7, 0)
A) x2 4 - y2 49 = 1 B) x2 49 - y2 4 = 1 C) x2 4 - y2 45 = 1 D) x2 45 - y2 4 = 1
- Vertices at (0, ±6), foci at (0, ±9)
A) y 81
= 1 B) y 45
= 1 C) y 36
= 1 D) y 36
- Foci at (±8, 0), transverse axis with length 14
A) x 49
= 1 B) x 49
= 1 C) x 64
= 1 D) x 15
- Vertices at (0, ±6), asymptotes at y = ± 3 7
x
A) y 36
= 1 B) y 49
= 1 C) y 196
= 1 D) y 36
- Foci at (0, ±7), a conjugate axis with length 10
A) y 49
= 1 B) y 24
= 1 C) y 100
= 1 D) y 25
- Center (4, - 3), focus (9, - 3), vertex (7, - 3)
A) (x^ - 9 4)2- (y^ + 25 3)2 = 1 B) (x^ - 16 4)2 - (y^ + 9 3)2 = 1
C) (x^ +^ 4) 9
= 1 D) (x^ -^ 4) 9
Answer Key
Testname: 12_HYPERBOLAS
1) B
2) D
3) B
4) A
5) D
6) B
7) C
8) B
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
- C
- D
- B
- A
- B
- D
- A
- C
