AnswersCUSD Advanced Math A 5.0Graphing Polar Equations

Graphing Polar Equations — Unit test Answers

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The center of a hyperbola is located at the origin. One focus is located at (0, 20), and its associated directrix is represented by the line y = . What is the equation of the hyperbola?

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
2
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Which equation represents a hyperbola?

A
4x2 + 3x + 4y2+ 5 = 0
B
2x2 – 5xy + 4y2 + 10x – y + 12 = 0
C
3x2 – 6xy + 3y2 + 5x – 2y + 1 = 0
D
3x2 + xy – 9y2 + 2x + 5 = 0
3

Which rectangular equation represents the parametric equations x = 3 and y = 6t?

Question illustration
A
y = 2x2, for x ≥ 0
B
y = x2, for x ≥ 0
Option B
C
y = 54x2, for x ≥ 0
D
y = x2, for x ≥ 0
Option D
4

The cable for a certain suspension bridge is modeled by a parabola with vertex (0, 0) 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 = StartFraction 1 Over 3,000 EndFraction x squared
Option A
B
y = StartFraction 1 Over 750 EndFraction x squared
Option B
C
y = StartFraction 1 Over 25 EndFraction x squared
Option C
D
y = StartFraction 1 Over 6 EndFraction x squared
Option D
5

Question text not available

Question illustration
A
(1,−2)
B
(1, 1)
C
(1, 3)
D
(1, 6)
6

A graphic designer creates a logo in the shape of an ellipse. The equation , with units in centimeters, represents the outer edge of the logo. How tall is the logo?

Question illustration
A
3.8 cm
B
7.6 cm
C
8 cm
D
16 cm
7

Question text not available

Question illustration
A
points G and H ✓ Correct
B
points J and K
C
points L and N
D
points M and N
8

Convert –2y2 + x – 4y + 6 = 0 into standard form.

A
x = 2(y + 1)2 – 6
B
x = 2(y + 1)2 – 8
C
x = 2(y + 1)2 – 7
D
x = 2(y + 1)2 + 8
9

Question text not available

Question illustration
A
x = −4.25 and x = 8.25
B
x = −3.25 and x = 9.25 ✓ Correct
C
y = −4.25 and y = 8.25
D
y = −3.25 and y = 9.25
10

In a video game, two objects move around the screen according to the equations r = 4cos(θ) and r = –1 + 2cos(θ). Which coordinates represent a possible collision point of the objects?

A
(Negative 2, StartFraction 2 pi Over 3 EndFraction)
Option A
B
(Negative 2, StartFraction 5 pi Over 6 EndFraction)
Option B
C
(2, StartFraction 2 pi Over 3 EndFraction)
Option C
D
(2, StartFraction 5 pi Over 6 EndFraction)
Option D
11

What are the vertices of the hyperbola whose equation is = 1?

Question illustration
A
(−13, 8) and (−1, 8)
B
(−12, 8) and (−2, 8)
C
(−7, 2) and (−7, 14)
D
(−7, 3) and (−7, 13)
12

Which graph represents points on the polar curve r = 2 + 5sin(θ)?

A
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).
Option A
B
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).
Option B
C
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).
Option C
D
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).
Option D
13

A yard dart is thrown from a height of 3 feet with an initial velocity of 25 feet per second at an elevation angle of 70°. How long is the dart in the air? Round to the nearest tenth.

A
0.7 seconds
B
0.8 seconds
C
1.5 seconds
D
1.6 seconds
14

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

A
circle
B
ellipse
C
hyperbola
D
parabola
15

Which graph represents the hyperbola = 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

A parabola has the following properties.Vertex at (–2, 1)Directrix is x = 5Which equation represents this parabola?

A
(x + 2) = (y – 1)2
B
28(x + 2) = (y – 1)2
C
–28(x + 2) = (y – 1)2
D
(x + 2) = (y – 1)2
17

What is the radius of the circle with equation ?

Question illustration
A
unit
B
units
C
unit
D
units
18

The graph of a hyperbola is shown.

Question illustration
A
(0, −4)
B
(−3, 0)
C
(0, 0)
D
(0, 5)
19

Convert the equation –9x2 + 25y2 – 100y – 125 = 0 into standard form.

A
StartFraction (y + 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1
B
StartFraction (y minus 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1
C
StartFraction (y minus 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1
D
StartFraction (y + 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1
20

The equation (x + 11)2 + (y – 27)2 = 2.25, with units in yards, represents a circular fountain in a park. The park entrance maps to (0, 0). 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 north
B
11 yards west and 27 yards north
C
11 yards east and 27 yards south
D
11 yards west and 27 yards south

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