AnswersPrecalculusModeling with Conic Sections and Polar Equations

Modeling with Conic Sections and Polar Equations — Test Answers

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1
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What is the conjugate of z ?

A
7 minus 6 i
B
6 minus 7 i
C
negative 7 plus 6 i
D
negative 6 plus 7 i
2
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Which points are the vertices of the ellipse?

A
points cap g and cap h
B
points cap l and cap n
C
points cap j and cap k
D
points cap m and cap n
5

What are the vertices of the hyperbola whose equation is the fraction with numerator open paren x plus 7 close paren squared and denominator 25 minus the fraction with numerator open paren y minus 8 close paren squared and denominator 36 is equal to 1 ?

A
open paren negative 12 comma 8 close paren and open paren negative 2 comma 8 close paren
B
open paren negative 7 comma 2 close paren and open paren negative 7 comma 14 close paren
C
open paren negative 7 comma 3 close paren and open paren negative 7 comma 13 close paren
D
open paren negative 13 comma 8 close paren and open paren negative 1 comma 8 close paren
6

What are the foci of the hyperbola whose equation is the fraction with numerator open paren y minus 2 close paren squared and denominator 64 minus the fraction with numerator open paren x minus 4 close paren squared and denominator 36 is equal to 1 ?

A
open paren 4 comma negative 8 close paren and open paren 4 comma 12 close paren
B
open paren 4 comma negative 6 close paren and open paren 4 comma 10 close paren
C
open paren negative 6 comma 2 close paren and open paren 14 comma 2 close paren
D
open paren negative 4 comma 2 close paren and open paren 12 comma 2 close paren
7

Which graph represents the hyperbola the fraction with numerator x squared and denominator 3 squared minus the fraction with numerator y squared and denominator 8 squared is equal to 1 ?

A
Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (0 comma negative 3) and (0 comma 3). The branches of the hyperbola open up and down. A dashed box is shown around the points (negative 8 comma 0), (0 comma 3), (8 comma 0), and (0 comma negative 3).
B
Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (0 comma negative 8) and (0 comma 8). The branches of the hyperbola open up and down. A dashed box is shown around the points (negative 3 comma 0), (0 comma 8), (3 comma 0), and (0 comma negative 8).
C
Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (negative 8 comma 0) and (8 comma 0). The branches of the hyperbola open left and right. A dashed box is shown around the points (negative 8 comma 0), (0 comma 3), (8 comma 0), and (0 comma negative 3).
D
Image with description A four-quadrant coordinate plane. A hyperbola is shown centered at the origin. The transverse axis has endpoints at (negative 3 comma 0) and (3 comma 0). The branches of the hyperbola open left and right. A dashed box is shown around the points (negative 3 comma 0), (0 comma 8), (3 comma 0), and (0 comma negative 8).
8

Convert negative 2 y squared plus x minus 4 y plus 6 is equal to 0 into standard form.

A
x is equal to 2 times open paren y plus 1 close paren squared minus 7
B
x is equal to 2 times open paren y plus 1 close paren squared minus 6
C
x is equal to 2 times open paren y plus 1 close paren squared minus 8
D
x is equal to 2 times open paren y plus 1 close paren squared plus 8
14

Which equation represents a hyperbola?

A
2 x squared minus 5 x y plus 4 y squared plus 10 x minus y plus 12 is equal to 0
B
4 x squared plus 3 x plus 4 y squared plus 5 is equal to 0
C
3 x squared plus x y minus 9 y squared plus 2 x plus 5 is equal to 0
D
3 x squared minus 6 x y plus 3 y squared plus 5 x minus 2 y plus 1 is equal to 0
15

Which graph is represented by the equation open paren x plus 3 close paren squared plus open paren y minus 4 close paren squared is equal to 9 ?

A
Image with description On a coordinate plane, a circle has center (negative 3, 4) and radius 9.
B
Image with description On a coordinate plane, a circle has center (negative 3, 4) and radius 3.
C
Image with description On a coordinate plane, a circle has center (3, negative 4) and radius 9.
D
Image with description On a coordinate plane, a circle has center (3, negative 4) and radius 3.
18

Which equation represents the rectangular form of r is equal to 4 cosine theta ?

A
open paren x minus 2 close paren squared plus y squared is equal to 4
B
open paren x plus 2 close paren squared plus y squared is equal to 0
C
open paren x plus 2 close paren squared plus y squared is equal to 4
D
open paren x minus 2 close paren squared plus y squared is equal to 0
19

Which graph represents points on the polar curve r is equal to 2 plus 5 sine theta ?

A
Image with description On a polar coordinate plane, points are at (0, 0), (2, 0), (negative 2, pi), (3, StartFraction 3 pi Over 2 EndFraction), (7, StartFraction 3 pi Over 2 EndFraction).
B
Image with description On a polar coordinate plane, points are at (0, 0), (2, StartFraction pi Over 2 EndFraction), (2, StartFraction 3 pi Over 2 EndFraction), (3, pi), (7, pi).
C
Image with description On a polar coordinate plane, points are at (0, 0), (2, 0), (negative 2, pi), (3, StartFraction pi Over 2 EndFraction), (7, StartFraction pi Over 2 EndFraction).
D
Image with description On a polar coordinate plane, points are at (0, 0), (2, StartFraction pi Over 2 EndFraction), (2, StartFraction 3 pi Over 2 EndFraction), (3, 0), (7, 0).
20

For the complex number z=(5⁢sqrt(3))/(4)−(5)/(4)⁢i , what is the polar form?

A
z=54(cos⁡(π6)+i⁢sin⁡(π6)
B
z=52(cos⁡(11⁢π6)+i⁢sin⁡(11⁢π6)
C
z=52(cos⁡(π6)+i⁢sin⁡(π6)
D
z=54(cos⁡(11⁢π6)+i⁢sin⁡(11⁢π6)

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