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
3

Which point has coordinates open paren 5 comma negative 7 pi over 6 close paren ?

A
point cap d
B
point cap A
C
point cap c
D
point cap b
4

A graphic designer creates a logo in the shape of an ellipse. The equation the fraction with numerator x squared and denominator 64 plus the fraction with numerator y squared and denominator 14 point 4 4 is equal to 1 , with units in centimeters, represents the outer edge of the logo. How tall is the logo?

A
16 cm
B
3 point 8 cm
C
8 cm
D
7 point 6 cm
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
9

A plane intersecting a double-napped cone is parallel to the generator. Which conic section is formed?

A
parabola
B
circle
C
hyperbola
D
ellipse
10

The cable for a certain suspension bridge is modeled by a parabola with vertex open paren 0 comma 0 close paren at the center of the bridge. At a point that is 150 ft from the center of the bridge, the height of the cable is 30 ft. Which equation represents the height of the cable at a distance x feet from the center?

A
y is equal to 1 over 750 x squared
B
y is equal to 1 over 25 x squared
C
y is equal to the fraction with numerator 1 and denominator 3 comma 000 x squared
D
y is equal to 1 sixth x squared
11

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by open paren x minus 2 close paren squared is equal to 10 times open paren y minus 3 close paren , where x and y are measured in inches. Where is the focus of the flashlight?

A
open paren 2 comma negative 5 point 5 close paren
B
open paren 5 point 5 comma 2 close paren
C
open paren 2 comma 5 point 5 close paren
D
open paren negative 2 comma negative 0 point 5 close paren
12

Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. The vertex of the parabola is at the origin. Where should Gabe place the bulb to ensure a perfect beam of light?

A
open paren 1 comma 0 close paren
B
open paren 4 comma 0 close paren
C
open paren 0 comma 1 close paren
D
open paren 0 comma 4 close paren
13

What is the radius of the circle with equation open paren x plus 1 fifth close paren squared plus open paren y minus 2 fifths close paren squared is equal to 1 over 25 ?

A
2 over 25 units
B
1 fifth unit
C
2 fifths units
D
1 over 25 unit
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.
16

Aramis is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by open paren x minus 4 close paren squared is equal to 3 times open paren y minus 3 close paren , where x and y are measured in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. Where should the feed antenna be placed?

A
0 point 7 5 in. to the right of the vertex
B
0 point 7 5 in. below the vertex
C
0 point 7 5 in. above the vertex
D
0 point 7 5 in. to the left of the vertex
17

The equation open paren x plus 11 close paren squared plus open paren y minus 27 close paren squared is equal to 2 point 2 5 , with units in yards, represents a circular fountain in a park. The park entrance maps to open paren 0 comma 0 close paren If the positive x -axis represents east and the positive y -axis represents north, what is the location of the fountain relative to the park entrance?

A
11 yards east and 27 yards south
B
11 yards east and 27 yards north
C
11 yards west and 27 yards south
D
11 yards west and 27 yards north
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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