Answers25-26 TX-Precalculus BPerformance Task: Graphing Conic Sections

Performance Task: Graphing Conic Sections — Unit test Answers

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1
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Question text not available

Question illustration
A
x = −4.6 and x = 4.6
B
x = −3.5 and x = 3.5
C
y = −4.6 and y = 4.6
D
y = −3.5 and y = 3.5
2
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Review the graph of circle A.

Question illustration
A
(x – 1)2 + (y – 1)2 = 5
B
(x + 1)2 + (y + 1)2 = 5
C
(x – 1)2 + (y – 1)2 = 25
D
(x + 1)2 + (y + 1)2 = 25
3

Which is the equation of an asymptote of the hyperbola whose equation is = 1?

Question illustration
A
y = −3x − 5
B
y = −3x − 7
C
y = 3x − 5
D
y = 3x + 7
4

What is the positive slope of the asymptote of = 1? The positive slope of the asymptote is .

Answer not available
5

The graph of a hyperbola is shown.

Question illustration
A
9 units
B
12 units
C
18 units
D
24 units
6

Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?

A
On a coordinate plane, a curve starts at (1, 0) and curves up through (0, 2) to (negative 24, 10).
Option A
B
On a coordinate plane, a curve starts at (1, 0) and curves down through (0, negative 2) to (negative 24, negative 10).
Option B
C
On a coordinate plane, a curve starts at (1, 0) and curves down through (2, negative 2) to (26, negative 10).
Option C
D
On a coordinate plane, a curve starts at (1, 0) and curves up through (2, 2) to (26, 10).
Option D
7

What is the rectangular form of the parametric equations x = 6t and y =?

Question illustration
A
y = StartFraction x squared Over 4 EndFraction
Option A
B
y = StartFraction x squared Over 9 EndFraction
Option B
C
y = StartFraction x Over 144 EndFraction
Option C
D
y = StartFraction x Over 9 EndFraction
Option D
8

What is the diameter of a circle with the equation (x – 4)2 + (y + 6)2 = 64?

A
4
B
8
C
16
D
64
9

A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.

Question illustration
A
4 km west and 12 km south
B
6 km west and 4 km north
C
2 km east and 10 km north
D
6 km east and 8 km north
10

Which graph represents the solution to the system of inequalities?

Question illustration
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and below the curve is shaded.
Option A
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and above the curve is shaded.
Option B
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (8, 0), (0, negative 4), (negative 8, 0) and (0, 4). Everything inside of the ellipse and below the curve is shaded.
Option C
D
Option
Option D
11

An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). The equation of the ellipse is in the form below.

Question illustration
A
12
B
16
C
20
D
24
12

The foci and the vertices of the hyperbola are labeled.

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
13

Question text not available

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
14

A mirror has a parabolic surface defined by the equation y = x2 with the vertex (0, 0) at the center of the mirror. When the width of the mirror is 8 inches, what is the depth, y, of the mirror?

Question illustration
A
in.
Option A
B
in.
Option B
C
in.
Option C
D
in.
Option D
15

Which image shows a plane slicing a double-napped cone to produce a hyperbola?

A
2 cones are stacked at their points. A horizontal plane goes through the center of a cone.
Option A
B
2 cones are stacked at their points. A plane goes diagonally through the center of a cone.
Option B
C
2 cones are stacked at their points. A plane goes diagonally along the sides of the cones.
Option C
D
2 cones are stacked at their points. A plane goes diagonally through both cones.
Option D

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