Quiz about PreCal 8.3 Hyperbolas Quiz Review

Question 1

What is the length of the conjugate and transverse axes of the hyperbola:

$$\frac{x^2}{25}-\frac{y^2}{144}=1$$

Accepted Answer

conjugate axis length: 24

transverse axis length: 10

Answer

conjugate axis length: 10

transverse axis length: 12

Answer

conjugate axis length: 10

transverse axis length: 24

Answer

conjugate axis length: 5

transverse axis length: 12

Question 2

Given the equation of the hyperbola (find its center, transverse and conjugate axis lengths to) match it to its correct graph.

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

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 3

What is the equation, in standard form, of the graph of the hyperbola shown?

Accepted Answer

$$\frac{\left(x+3\right)^2}{16}-\frac{\left(y-1\right)^2}{4}=1$$

Answer

$$\frac{\left(x+3\right)^2}{16}+\frac{\left(y-1\right)^2}{4}=1$$

Answer

$$\frac{\left(x-3\right)^2}{8}-\frac{\left(y+1\right)^2}{4}=1$$

Answer

$$\frac{\left(x-1\right)^2}{4}-\frac{\left(y+3\right)^2}{8}=1$$

Question 4

Find the co-vertices of the hyperbola defined by the equation:

$$\frac{\left(y-4\right)^2}{4}-\frac{\left(x+6\right)^2}{49}=1$$

Accepted Answer

(1, 4) & (-13, 4)

Answer

(11, 4) & (-3, 4)

Answer

(-4, -6) & (-8, -6)

Answer

(6, -6) & (2, -6)

Question 5

Find the equations of the asymptotes of the hyperbola defined by the equation:

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$y=\pm\frac{2}{3}\left(x+3\right)+1$$

Question 6

Find an equation in standard form for the hyperbola that satisfies the given conditions:

transverse axis endpoints: (-3, 5) & (-3, -1)

slope of one asymptote: 3/2

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

Find an equation in standard form for the hyperbola that satisfies the given conditions:

transverse axis endpoints: (1, 1) & (-7, 1)

conjugate axis length: 4

Accepted Answer

$$\frac{\left(x+3\right)^2}{16}-\frac{\left(y-1\right)^2}{4}=1$$

Answer

$$\frac{\left(x+3\right)^2}{16}+\frac{\left(y-1\right)^2}{4}=1$$

Answer

$$\frac{\left(y-1\right)^2}{4}-\frac{\left(x+3\right)^2}{16}=1$$

Answer

$$\frac{\left(x+3\right)^2}{4}-\frac{\left(y-1\right)^2}{16}=1$$

Question 8

Find an equation in standard form for the hyperbola that satisfies the given conditions:

foci: (-4, 2) & (2, 2)

transverse axis endpoints: (-3, 2) & (1, 2)

Accepted Answer

$$\frac{\left(x+1\right)^2}{4}-\frac{\left(y-2\right)^2}{5}=1$$

Answer

$$\frac{\left(x+1\right)^2}{4}-\frac{\left(y-2\right)^2}{25}=1$$

Answer

$$\frac{\left(x-1\right)^2}{4}-\frac{\left(y-2\right)^2}{5}=1$$

Answer

$$\frac{\left(x+1\right)^2}{5}-\frac{\left(y-2\right)^2}{4}=1$$

PreCal 8.3 Hyperbolas Quiz Review

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