Quiz about Hyperbolas

Question 1

What are the values of a and b:

$$\frac{\left(x+1\right)^2}{9}-\frac{\left(y-3\right)^2}{4}=1$$

Accepted Answer

a = 3, b = 2

Answer

a = 1, b = 2

Answer

a = 9, b = 4

Answer

a = 25, b = 10

Question 2

What is the formula for finding the value of c in a hyperbola?

Accepted Answer

c² = a² + b²

Answer

c² = a² - b²

Answer

4p

Answer

(x-h)² + (y-k)² = r²

Question 3

The branches of the hyperbola with the equation $$\frac{\left(y-4\right)^2}{16}-\frac{\left(x+4\right)^2}{25}=1$$ open in which directions?

Accepted Answer

up and down

Answer

left and right

Answer

this is not a hyperbola

Question 4

Identify the vertices of the hyperbola:

$$\frac{\left(y+1\right)^2}{4}-\frac{\left(x-2\right)^2}{9}=1$$

Accepted Answer

(2, 1) and (2, -3)

Answer

(4, -1) and (0, -1)

Answer

(3, 2) and (-1, 2)

Answer

(1, -2) and (-3, -2)

Question 5

Identify the center of the hyperbola:

$$\frac{x^2}{16}-\frac{\left(y+2\right)^2}{4}=1$$

Accepted Answer

(0, -2)

Answer

(4, 2)

Answer

(0, 2)

Answer

(-2, 0)

Question 6

Which of the following is the graph of the hyperbola defined by:

$$\frac{x^2}{9}-\frac{y^2}{25}=1$$

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Question 7

Write the equation of the hyperbola:

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

Length of conjugate axis = 16 units

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

Write the equation of the hyperbola given:

Vertices: (8, 8) and (-6, 8)

Foci: $$\left(1\pm7\sqrt[]{2},\ 8\right)$$

Accepted Answer

$$\frac{\left(x-1\right)^2}{49}-\frac{\left(y-8\right)^2}{49}=1$$

Answer

$$\frac{\left(y-8\right)^2}{49}-\frac{\left(x-1\right)^2}{49}=1$$

Answer

$$\frac{\left(y+8\right)^2}{49}-\frac{\left(x-1\right)^2}{49}=1$$

Answer

$$\frac{\left(y+1\right)^2}{49}-\frac{\left(x+8\right)^2}{49}=1$$

Question 9

Write the equation of the hyperbola given:

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

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 10

Write the equation of the hyperbola given:

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

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

Rewrite the following hyperbola's equation in standard form:

$$9x^2-y^2+54x+16y-64=0$$

Accepted Answer

$$\frac{\left(x+3\right)^2}{9}-\frac{\left(y-8\right)^2}{81}=1$$

Answer

$$\frac{\left(x+3\right)^2}{81}-\frac{\left(y-8\right)^2}{9}=1$$

Answer

$$\frac{\left(y-8\right)^2}{81}-\frac{\left(x+3\right)^2}{9}=1$$

Answer

$$\frac{\left(y+8\right)^2}{81}-\frac{\left(x-3\right)^2}{9}=1$$

Hyperbolas

14 questions

The length of the transverse axis is equal to _____

The length of the conjugate axis is equal to _____

The distance from the center to the focus point is represented by _____

What is the formula for finding the value of c in a hyperbola?

Write the equation of the hyperbola:
Vertices: (5, 14) and (5, -4)
Length of conjugate axis = 16 units

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Hyperbolas

14 questions

The length of the transverse axis is equal to _____

The length of the conjugate axis is equal to _____

The distance from the center to the focus point is represented by _____

What is the formula for finding the value of c in a hyperbola?

Write the equation of the hyperbola:Vertices: (5, 14) and (5, -4)Length of conjugate axis = 16 units

Create a free account and access millions of resources

Similar Resources on Wayground

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Write the equation of the hyperbola:
Vertices: (5, 14) and (5, -4)
Length of conjugate axis = 16 units