Question 1

Find the polar equation for the conic that has its focus at the pole and its directrix is   units to the right of the pole and its eccentricity is   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Identify the conic section by transforming to rectangular coordinates.

Accepted Answer

A circle through the

Question 3

Rotate the coordinate axes to remove the xy-term. What is the equation in the new   coordinate system? What type of conic section is it?

Accepted Answer

The answer of Rotate the coordinate axes to remove the...

Question 4

For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of   at t = 4 is

Accepted Answer

A)  2 
B)  9 
C)  4 
D)  3 
E)  0 
A)  2 
B)  9 
C)  4 
D)  3 
E)  0

Question 5

Rotate the coordinates to remove the xy-term. Then, name the conic.

Accepted Answer

A)  circle 
B)  hyperbola 
C)  ellipse 
D)  parabola 
A)  circle 
B)  hyperbola 
C)  ellipse 
D)  parabola

Question 6

Find the intersection point(s) of the circle   and the cardioid   for

Accepted Answer

A)    
B)    and
  
C)    and
  
D)    and
  
E)  There are none 
A)    
B)    and
  
C)    and
  
D)    and
  
E)  There are none

Question 7

Express the given curve in polar coordinates.

Accepted Answer

The answer of Express the given curve in polar coordinates....

Question 8

For the parametric curve:   ,   , eliminate the parameter and express in rectangular form.

Accepted Answer

A)  x2 + y2 = 1 
B)    
C)    
D)    
E)    
A)  x2 + y2 = 1 
B)    
C)    
D)    
E)

Question 9

Find the area inside the circle   , and to the right of the line   .

Accepted Answer

The answer of Find the area inside the circle ...

Question 10

For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Create the parametric equation to describe a circle of radius 13 oriented clockwise.

Accepted Answer

x = 13 sin

Question 12

Find the area of the region that is common to   and   .

Accepted Answer

The answer of Find the area of the region that...

Question 13

Find the polar equation for the conic that has its focus at the pole and its directrix is   units above the pole and its eccentricity is   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Express the given curve in polar coordinates.

Accepted Answer

The answer of Express the given curve in polar coordinates....

Question 15

Find the foci of the ellipse   in the x'y'-coordinate system.

Accepted Answer

The answer of Find the foci of the ellipse ...

Question 16

Sketch the curve in polar coordinates.

Accepted Answer

The answer of Sketch the curve in polar coordinates. ...

Question 17

Express the given curve in polar coordinates.

Accepted Answer

The answer of Express the given curve in polar coordinates....

Question 18

Sketch the curve in polar coordinates.

Accepted Answer

The answer of Sketch the curve in polar coordinates. ...

Question 19

For the parametric curve: x = 4t2, y = 4t, eliminate the parameter and express in rectangular form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Find the ends of the minor axis of the ellipse   in the x'y'-coordinate system.

Accepted Answer

The answer of Find the ends of the minor axis...

Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is .

Identify the conic section by transforming to rectangular coordinates.

Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of at t = 4 is

Rotate the coordinates to remove the xy-term. Then, name the conic.

Find the intersection point(s) of the circle and the cardioid for

Express the given curve in polar coordinates.

For the parametric curve: , , eliminate the parameter and express in rectangular form.

Find the area inside the circle , and to the right of the line .

For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form.

Create the parametric equation to describe a circle of radius 13 oriented clockwise.

Find the area of the region that is common to and .

Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is .

Express the given curve in polar coordinates.

Find the foci of the ellipse in the x'y'-coordinate system.

Sketch the curve in polar coordinates.

Express the given curve in polar coordinates.

Sketch the curve in polar coordinates.

For the parametric curve: x = 4t², y = 4t, eliminate the parameter and express in rectangular form.

Find the ends of the minor axis of the ellipse in the x'y'-coordinate system.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 10: Parametric and Polar Curves; Conic Sections

Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is .

Identify the conic section by transforming to rectangular coordinates.

Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of at t = 4 is

Rotate the coordinates to remove the xy-term. Then, name the conic.

Find the intersection point(s) of the circle and the cardioid for

Express the given curve in polar coordinates.

For the parametric curve: , , eliminate the parameter and express in rectangular form.

Find the area inside the circle , and to the right of the line .

For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form.

Create the parametric equation to describe a circle of radius 13 oriented clockwise.

Find the area of the region that is common to and .

Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is .

Express the given curve in polar coordinates.

Find the foci of the ellipse in the x'y'-coordinate system.

Sketch the curve in polar coordinates.

Express the given curve in polar coordinates.

Sketch the curve in polar coordinates.

For the parametric curve: x = 4t2, y = 4t, eliminate the parameter and express in rectangular form.

Find the ends of the minor axis of the ellipse in the x'y'-coordinate system.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

For the parametric curve: x = 4t², y = 4t, eliminate the parameter and express in rectangular form.