Question 1

Graph the conic section.
-$$x ^ { 2 } - 4 y - 4 x = 0$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-\[x ^ { 2...

Question 2

Graph the conic section.
-$36(x+2)^{2}+25(y-2)^{2}=900$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-$36(x+2)^{2}+25(y-2)^{2}=900$

A)

B)

C)

D)

...

Question 3

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( - 3,0 )$ is one-fourth of the distance from the line $x = - 11$.
A) Hyperbola
B) Parabola
C) Circle
D) Ellipse

Accepted Answer

The given condition describes an ellipse, where the distance from a fixed point (focus) is a constant fraction of the distance from a fixed line (directrix).

Question 4

Find the eccentricity of the conic section shown in the graph.
-
A) $\mathrm { e } = 1$
B) $e = \frac { 21 } { 5 }$
C) $\mathrm { e } = \frac { \sqrt { 29 } } { 5 }$
D) $\mathrm { e } = \frac { 29 } { 2 }$

Accepted Answer

The answer of Find the eccentricity of the conic section...

Question 5

Graph the conic section.
-
A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-
A)

B)

C)

D)

...

Question 6

Graph the conic section.
-
A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-
A)

B)

C)

D)

...

Question 7

Find the eccentricity of the conic section shown in the graph.
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A) $e = \frac { 4 \sqrt { 3 } } { 3 }$
B) $e = 1$
C) $\mathrm { e } = \frac { \sqrt { 3 } } { 4 }$
D) $\mathrm { e } = \sqrt { 3 }$

Accepted Answer

The answer of Find the eccentricity of the conic section...

Question 8

Graph the conic section.
-

A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-

A)

B)

C)

D)

...

Question 9

Find the eccentricity of the conic section shown in the graph.
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A) $\mathrm { e } = \frac { 1 } { 2 }$
B) $\mathrm { e } = 3$
C) $\mathrm { e } = 1$
D) $\mathrm { e } = 2$

Accepted Answer

The answer of Find the eccentricity of the conic section...

Question 10

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points $( 0,9 )$ and $( 0 , - 9 )$ is 4 .
A) Circle
B) Hyperbola
C) Ellipse
D) Parabola

Accepted Answer

This description matches the definition of a hyperbola, which is the set of all points in the plane where the absolute value of the difference of the distances from two fixed points (the foci) is a constant. In this case, the two fixed points are $(0,9)$ and $(0,-9)$, and the constant difference is 4.

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Suppose that $\mathrm { A } = \mathrm { C } \neq 0$ in the equation $\mathrm { Ax } { } ^ { 2 } + \mathrm { Bx } + \mathrm { Cy } { } ^ { 2 } + \mathrm { Dy } + \mathrm { E } = 0$. What kind of graph does this equation have?

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Graph the conic section.
-
A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-
A)

B)

C)

D)

...

Question 13

Find the eccentricity of the conic section shown in the graph.
-$$x = - 21$$

A) $e = \frac { 5 } { 2 }$
B) $e = \frac { \sqrt { 21 } } { 5 }$
C) $e = \frac { \sqrt { 29 } } { 5 }$
D) $\mathrm { e } = 1$

Accepted Answer

The answer of Find the eccentricity of the conic section...

Question 14

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( 0,11 )$ is twice the distance from the line $y = 7$.
A) Ellipse
B) Circle
C) Parabola
D) Hyperbola

Accepted Answer

This is a hyperbola because the set of points where the distance to a point is a constant multiple (other than 1) of the distance to a line forms a hyperbola.

Question 15

When a satellite is near Earth, its orbital trajectory may trace out a hyperbola, a parabola, or an ellipse. The type of trajectory depends on the satellite's velocity $V$ in meters per second. It will be hyperbolic if $V > \frac { k } { \sqrt { D } }$, parabolic if $V =$ $\frac { k } { \sqrt { D } }$, and elliptical if $V < \frac { k } { \sqrt { D } }$, where $k = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem.
-When a certain satellite was at a maximum distance of 61.7 × 106 m from Earthʹs center, it had a velocity of 5668 m per sec. Determine the shape of its trajectory.
A) parabolic
B) hyperbolic
C) elliptical

Accepted Answer

The answer of When a satellite is near Earth, its...

Question 16

Find the eccentricity of the conic section shown in the graph.
-
Point A: $( - 9,0 )$
Point B: $( \sqrt { 85 } , 0 )$
Point $C : \left( \frac { 9 \sqrt { 13 } } { 2 } , 3 \right)$
A) $\mathrm { e } = \frac { 9 } { \sqrt { 85 } }$
B) $e = \frac { \sqrt { 85 } } { 9 }$
C) $\mathrm { e } = \frac { \sqrt { 85 } } { 81 }$
D) $\mathrm { e } = \frac { \sqrt { 77 } } { 9 }$

Accepted Answer

The answer of Find the eccentricity of the conic section...

Question 17

Graph the conic section.
-

A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-

A)

B)

C)

D)

...

Question 18

Find the eccentricity of the conic section shown in the graph.
-
A) $\mathrm { e } = \frac { \sqrt { 17 } } { 4 }$
B) $e = \frac { 4 } { \sqrt { 17 } }$
C) $\mathrm { e } = 1$
D) $\mathrm { e } = 4$

Accepted Answer

The answer of Find the eccentricity of the conic section...

Question 19

Graph the conic section.
-$3 x^{2}+4 y^{2}-36 x+40 y+196=0$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the conic section.
-\(3 x^{2}+4 y^{2}-36 x+40...

Question 20

When a satellite is near Earth, its orbital trajectory may trace out a hyperbola, a parabola, or an ellipse. The type of trajectory depends on the satellite's velocity $V$ in meters per second. It will be hyperbolic if $V > \frac { k } { \sqrt { D } }$, parabolic if $V =$ $\frac { k } { \sqrt { D } }$, and elliptical if $V < \frac { k } { \sqrt { D } }$, where $k = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem.
-If a satellite is scheduled to leave Earthʹs gravitational influence, its velocity must be increased so that its trajectory changes from elliptical to hyperbolic. Determine the minimum increase in
Velocity necessary for a satellite traveling at a velocity of 4881 meters per second to escape Earthʹs
Gravitational influence when D = 194 × 106 m.
A) 4817 m per sec
B) 4945 m per sec
C) 6906 m per sec
D) -2856 m per sec

Accepted Answer

The answer of When a satellite is near Earth, its...

Quiz 10: Analytic Geometry

Graph the conic section. - $x ^ { 2 } - 4 y - 4 x = 0$ $Graph the conic section. - x ^ { 2 } - 4 y - 4 x = 0 A) B) C) D)$

Graph the conic section. - $36(x+2) ^{2}+25(y-2) ^{2}=900$ $Graph the conic section. - 36(x+2) ^{2}+25(y-2) ^{2}=900 A) B) C) D)$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( - 3,0 )$ is one-fourth of the distance from the line $x = - 11$ .

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) \mathrm { e } = 1 B) e = \frac { 21 } { 5 } C) \mathrm { e } = \frac { \sqrt { 29 } } { 5 } D) \mathrm { e } = \frac { 29 } { 2 }$

Graph the conic section. -

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) e = \frac { 4 \sqrt { 3 } } { 3 } B) e = 1 C) \mathrm { e } = \frac { \sqrt { 3 } } { 4 } D) \mathrm { e } = \sqrt { 3 }$

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) \mathrm { e } = \frac { 1 } { 2 } B) \mathrm { e } = 3 C) \mathrm { e } = 1 D) \mathrm { e } = 2$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points $( 0,9 )$ and $( 0 , - 9 )$ is 4 .

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. - $x = - 21$ $Find the eccentricity of the conic section shown in the graph. - x = - 21 A) e = \frac { 5 } { 2 } B) e = \frac { \sqrt { 21 } } { 5 } C) e = \frac { \sqrt { 29 } } { 5 } D) \mathrm { e } = 1$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( 0,11 )$ is twice the distance from the line $y = 7$ .

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) \mathrm { e } = \frac { \sqrt { 17 } } { 4 } B) e = \frac { 4 } { \sqrt { 17 } } C) \mathrm { e } = 1 D) \mathrm { e } = 4$

Graph the conic section. - $3 x^{2}+4 y^{2}-36 x+40 y+196=0$ $Graph the conic section. - 3 x^{2}+4 y^{2}-36 x+40 y+196=0 A) B) C) D)$

Quiz 10: Analytic Geometry

Graph the conic section. - x2−4y−4x=0x ^ { 2 } - 4 y - 4 x = 0x2−4y−4x=0

Graph the conic section. - 36(x+2) 2+25(y−2) 2=90036(x+2) ^{2}+25(y-2) ^{2}=90036(x+2) 2+25(y−2) 2=900

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point (−3,0) ( - 3,0 ) (−3,0) is one-fourth of the distance from the line x=−11x = - 11x=−11 .

Find the eccentricity of the conic section shown in the graph. -

Graph the conic section. -

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. -

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. -

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points (0,9) ( 0,9 ) (0,9) and (0,−9) ( 0 , - 9 ) (0,−9) is 4 .

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. - x=−21x = - 21x=−21

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point (0,11) ( 0,11 ) (0,11) is twice the distance from the line y=7y = 7y=7 .

Find the eccentricity of the conic section shown in the graph. - Point A: (−9,0) ( - 9,0 ) (−9,0) Point B: (85,0) ( \sqrt { 85 } , 0 ) (85​,0) Point C:(9132,3) C : \left( \frac { 9 \sqrt { 13 } } { 2 } , 3 \right) C:(2913​​,3)

Graph the conic section. -

Find the eccentricity of the conic section shown in the graph. -

Graph the conic section. - 3x2+4y2−36x+40y+196=03 x^{2}+4 y^{2}-36 x+40 y+196=03x2+4y2−36x+40y+196=0

Graph the conic section. - $x ^ { 2 } - 4 y - 4 x = 0$ $Graph the conic section. - x ^ { 2 } - 4 y - 4 x = 0 A) B) C) D)$

Graph the conic section. - $36(x+2) ^{2}+25(y-2) ^{2}=900$ $Graph the conic section. - 36(x+2) ^{2}+25(y-2) ^{2}=900 A) B) C) D)$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( - 3,0 )$ is one-fourth of the distance from the line $x = - 11$ .

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) \mathrm { e } = 1 B) e = \frac { 21 } { 5 } C) \mathrm { e } = \frac { \sqrt { 29 } } { 5 } D) \mathrm { e } = \frac { 29 } { 2 }$

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) e = \frac { 4 \sqrt { 3 } } { 3 } B) e = 1 C) \mathrm { e } = \frac { \sqrt { 3 } } { 4 } D) \mathrm { e } = \sqrt { 3 }$

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) \mathrm { e } = \frac { 1 } { 2 } B) \mathrm { e } = 3 C) \mathrm { e } = 1 D) \mathrm { e } = 2$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points $( 0,9 )$ and $( 0 , - 9 )$ is 4 .

Find the eccentricity of the conic section shown in the graph. - $x = - 21$ $Find the eccentricity of the conic section shown in the graph. - x = - 21 A) e = \frac { 5 } { 2 } B) e = \frac { \sqrt { 21 } } { 5 } C) e = \frac { \sqrt { 29 } } { 5 } D) \mathrm { e } = 1$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( 0,11 )$ is twice the distance from the line $y = 7$ .

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - A) \mathrm { e } = \frac { \sqrt { 17 } } { 4 } B) e = \frac { 4 } { \sqrt { 17 } } C) \mathrm { e } = 1 D) \mathrm { e } = 4$

Graph the conic section. - $3 x^{2}+4 y^{2}-36 x+40 y+196=0$ $Graph the conic section. - 3 x^{2}+4 y^{2}-36 x+40 y+196=0 A) B) C) D)$