9.2 The Hyperbola

​9.2 The Hyperbola

Multiple Choice

What is the "a" value of this hyperbola? #12

• 5

• 6

• 3

• 4

• 7.5

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Multiple Choice

What are the vertices of the hyperbola? #5

• (0, 3) and (0, -3)

• (-4, 3) and (-4, -3)

• (0, 1) and (0, -1)

• (4, 0) and (-4, 0)

Multiple Choice

What is the equation describing the relationship between dimensions and foci of a hyperbola? #1

• c² = a² + b²

• c² = a² - b²

• 4p

• (x-h)² + (y-k)² = r²

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Multiple Choice

A hyperbola has vertices (±5, 0) and one focus at (6, 0). What is the equation of the hyperbola in standard form? #6

• x²/25 + y²/11 = 1

• x²/5 - y²/11 = 1

• x²/11- y²/25 = 1

• x²/25 - y²/11= 1

Multiple Choice

Find the equation of a hyperbola. #7

• (x - 2)² / 16 - (y + 3)² / 20 = 1

• (x + 3)² / 16 - (y - 2)² / 20 = 1

• (x - 2)² / 20 - (y + 3)² / 16 = 1

• (y + 3)² / 16 - (x - 2)² / 20 = 1

Multiple Choice

The vertices of a hyperbola are located at (1,1) and (5,1). Which are the coordinates of the center? #10

• (3,1)

• (3,0)

• (1,3)

• (9,1)

Multiple Choice

What is the "b" value of this hyperbola? #13

• 3

• 5

• 4

• 6

• 7.5

Multiple Choice

Is the hyperbola vertical or horizontal? #3

• Vertical

• Horizontal

Multiple Choice

What is the value of a² for the given hyperbola? #8

• 1

• 5

• 25

• 16

Multiple Choice

What are the foci of the hyperbola with the equation y²/12 - x²/5 = 1? #2

• (0, ±√17)

• (±√17, 0)

• (0, ±√7)

• (±√7, 0)

Multiple Choice

A hyperbola centered at (-3, 2) with a horizontal transverse axis has asymptotes y = ± ¾x.  Which of the following could be the equation of the hyperbola in standard form? #9

• (x + 3)²/16 + (y - 2)²/ 9 = 1

• (x + 3)²/ 4 - (y - 2)²/ 3 = 1

• (x + 3)²/16 - (y - 2)²/ 9 = 1

• (x + 3)²/ 9 - (y - 2)²/ 16 = 1

Multiple Choice

What is the eccentricity of the hyperbola? #17

• 1.17

• 1.38

• 2.25

• 3.14

• 0.89

Multiple Choice

What is the "c" value of this hyperbola? #14

• 5.83

• 4.45

• 3.34

• 6.5

• 7.25

Multiple Choice

What is the graph of this hyperbola? #16

Multiple Choice

Which graph represents $$\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$$  ? #21

Multiple Choice

Write the equation of the hyperbola: #22

Vertices: (5, 14) and (5, -4)

Length of conjugate axis = 16 units

• $$\frac{\left(y-5\right)^2}{81}-\frac{\left(x-5\right)^2}{64}=1$$  

• $$\frac{\left(y-5\right)^2}{64}-\frac{\left(x-5\right)^2}{81}=1$$  

• $$\frac{\left(x-5\right)^2}{64}-\frac{\left(y-5\right)^2}{81}=1$$  

• $$\frac{\left(y-5\right)^2}{81}-\frac{\left(x+5\right)^2}{64}=1$$  

Multiple Choice

Write the equation of the hyperbola given: #23

Vertices: (1, -3) and (-7, -3)

Asymptotes: $$y=\pm\frac{3}{2}\left(x+3\right)-3$$  

• $$\frac{\left(x+3\right)^2}{36}-\frac{\left(y+3\right)^2}{16}=1$$  

• $$\frac{\left(x+3\right)^2}{16}-\frac{\left(y+3\right)^2}{36}=1$$  

• $$\frac{\left(y+3\right)^2}{36}-\frac{\left(x+3\right)^2}{16}=1$$  

• $$\frac{\left(x+3\right)^2}{36}-\frac{\left(y-3\right)^2}{16}=1$$  

Multiple Choice

Write the equation of the hyperbola given: #24

Foci: $$\left(-1,2\pm\sqrt[]{265}\right)$$  

Eccentricity: $$e=\frac{\sqrt[]{265}}{11}$$  

• $$\frac{\left(x+1\right)^2}{121}-\frac{\left(y-2\right)^2}{144}=1$$  

• $$\frac{\left(y-2\right)^2}{121}-\frac{\left(x+1\right)^2}{144}=1$$  

• $$\frac{\left(y-2\right)^2}{9}-\frac{\left(x+1\right)^2}{100}=1$$  

• $$\frac{\left(y-2\right)^2}{121}-\frac{\left(x+1\right)^2}{9}=1$$