AnswersPrecalculusModeling with Conic Sections and Polar Equations

Practice Test Answers

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Which equation represents the rectangular form of theta is equal to 5 pi over 6 ?

A
square root of 3 x plus y is equal to 0
B
square root of 3 x minus y is equal to 0
C
square root of 3 x plus 3 y is equal to 0
D
square root of 3 x minus 3 y is equal to 0
4

Consider the polar curve r is equal to 4 sine 2 theta What is the length of each petal, and how many petals does the graph have?

A
The length of each petal is 4 , and the number of petals is 4 .
B
The length of each petal is 4 , and the number of petals is 2 .
C
The length of each petal is 2 , and the number of petals is 4 .
D
The length of each petal is 2 , and the number of petals is 2 .
5

Convert 9 x squared plus 4 y squared minus 54 x minus 8 y minus 59 is equal to 0 into standard form.

A
the fraction with numerator open paren x plus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y plus 1 close paren squared and denominator 36 is equal to 1
B
the fraction with numerator open paren x plus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y plus 1 close paren and denominator 9 is equal to 1
C
the fraction with numerator open paren x minus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y minus 1 close paren squared and denominator 36 is equal to 1
D
the fraction with numerator open paren x minus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y minus 1 close paren and denominator 9 is equal to 1
7

One focus of a hyperbola is located at open paren negative 1 comma 7 close paren One vertex of the hyperbola is located at open paren negative 1 comma 5 close paren The center is open paren negative 1 comma negative 3 close paren What is the equation of the hyperbola?

A
the fraction with numerator open paren y plus 3 close paren squared and denominator 64 minus the fraction with numerator open paren x plus 1 close paren squared and denominator 36 is equal to 1
B
the fraction with numerator open paren y minus 3 close paren squared and denominator 64 minus the fraction with numerator open paren x minus 1 close paren squared and denominator 36 is equal to 1
C
the fraction with numerator open paren y plus 1 close paren squared and denominator 64 minus the fraction with numerator open paren x plus 3 close paren squared and denominator 36 is equal to 1
D
the fraction with numerator open paren y minus 1 close paren squared and denominator 64 minus the fraction with numerator open paren x minus 3 close paren squared and denominator 36 is equal to 1
8

What are the conjugate and modulus of negative 14 minus 2 i ?

A
14 plus 2 i and 10 square root of 2
B
negative 14 plus 2 i and 10 square root of 2
C
negative 14 plus 2 i and 8 square root of 3
D
14 plus 2 i and 8 square root of 3
10

Which features describe the graph of the fraction with numerator y squared and denominator 96 squared minus the fraction with numerator x squared and denominator 40 squared is equal to 1 ? Choose two correct answers.

A
the center at open paren 0 comma 0 close paren
B
a focus at open paren 0 comma negative 96 close paren
C
a vertex at open paren 0 comma 96 close paren
D
a vertex at open paren negative 40 comma 0 close paren
E
a focus at open paren 104 comma 0 close paren
11

The equation the fraction with numerator y squared and denominator 100 plus the fraction with numerator x squared and denominator 4 is equal to 1 represents an ellipse. Which points are the vertices of the ellipse?

A
open paren negative 2 comma 0 close paren and open paren 2 comma 0 close paren
B
open paren 0 comma negative 2 close paren and open paren 0 comma 2 close paren
C
open paren negative 10 comma 0 close paren and open paren 10 comma 0 close paren
D
open paren 0 comma negative 10 close paren and open paren 0 comma 10 close paren
12

Which statements about the hyperbola are true? Choose three correct answers.

A
The transverse axis is vertical.
B
There is a vertex at open paren negative 2 comma 7 close paren .
C
The directrices are vertical lines.
D
There is a vertex at open paren negative 5 comma 2 close paren .
E
The center of the hyperbola is at open paren negative 2 comma 2 close paren .
13

She identified the conic as a circle with a center open paren 4 comma negative 2 close paren and a radius r is equal to 4 What error, if any, did Mariah make?

A
Mariah should have added 400 and 100 to the right side of the equation in step 4
B
Mariah did not make an error.
C
Mariah factored incorrectly in step 5. She should have factored to open paren x minus 8 close paren squared and open paren y plus 4 close paren squared .
D
Mariah listed the center incorrectly. The center should be open paren negative 4 comma 2 close paren .
14

Which graph shows the conjugate of z ?

A
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (5, negative 2).
B
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (2, negative 5).
C
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 5, 2).
D
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (2, 5).
15

Which is the standard form of the equation of the parabola shown in the graph?

A
y squared is equal to negative 4 x
B
x squared is equal to negative 4 y
C
x squared is equal to negative 16 y
D
y squared is equal to negative 16 x
16

What is the polar form of z ?

A
6 square root of 2 open paren cosine of open paren 225 degrees close paren plus i sine open paren 225 degrees close paren close paren
B
6 square root of 2 open paren cosine of open paren 135 degrees close paren plus i sine open paren 135 degrees close paren close paren
C
6 square root of 3 open paren cosine of open paren 225 degrees close paren plus i sine open paren 225 degrees close paren close paren
D
6 square root of 3 open paren cosine of open paren 135 degrees close paren plus i sine open paren 135 degrees close paren close paren
18

What is the equation for the hyperbola shown?

A
the fraction with numerator x squared and denominator 8 squared minus the fraction with numerator y squared and denominator 5 squared is equal to 1
B
the fraction with numerator y squared and denominator 5 squared minus the fraction with numerator x squared and denominator 8 squared is equal to 1
C
the fraction with numerator x squared and denominator 5 squared minus the fraction with numerator y squared and denominator 8 squared is equal to 1
D
the fraction with numerator y squared and denominator 8 squared minus the fraction with numerator x squared and denominator 5 squared is equal to 1

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