Question 1

Find the rectangular coordinates of the point whose polar coordinates are given.

Accepted Answer

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

Question 2

State the name that describes the polar curve most precisely.

Accepted Answer

A)  cardioid 
B)  lemniscate 
C)  line 
D)  circle 
E)  spiral 
A)  cardioid 
B)  lemniscate 
C)  line 
D)  circle 
E)  spiral

Question 3

Find the equation of the ellipse with a major axis length of   , a minor axis length of   , center at   , and foci on   .

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find the equation of the tangent to the curve   and   at   .

Accepted Answer

The answer of Find the equation of the tangent to...

Question 6

State the definition of a parabola. Use your definition to derive the equation of the parabola whose focus is at F(3, 9) and directrix x = 1.

Accepted Answer

Let P be a point on

Question 7

Put the rectangular equation y = 3x2 + 3 into parametric form.

Accepted Answer

A)  x = 3t, y = t2 + 3 
B)  x = t + 3, y = 3t2 
C)  x = t2, y = 3t2 + 3 
D)  x = t, y = 3t2 + 3 
E)  x = 3t2, y = t2 + 3 
A)  x = 3t, y = t2 + 3 
B)  x = t + 3, y = 3t2 
C)  x = t2, y = 3t2 + 3 
D)  x = t, y = 3t2 + 3 
E)  x = 3t2, y = t2 + 3

Question 8

Find the arclength of the curve   from   to

Accepted Answer

A)    
B)    
C)  3 
D)    
E)  4 
A)    
B)    
C)  3 
D)    
E)  4

Question 9

Find the equation of the hyperbola with vertices   and asymptotes   .

Accepted Answer

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

Question 10

Find the equation for the parabola whose directrix is y = 3 and vertex is at (-7, 2). Where is the focus located?

Accepted Answer

Since, p = -1, the e

Question 11

Find the arclength of the curve   from   to   .

Accepted Answer

The answer of Find the arclength of the curve ...

Question 12

Find the equation for the given graph when A = 3.

Accepted Answer

The answer of Find the equation for the given graph...

Question 13

If   the tangent to the curve at the origin is

Accepted Answer

A)  a horizontal line 
B)  a vertical line 
C)  the line   
D)  the line   
E)  the line   
A)  a horizontal line 
B)  a vertical line 
C)  the line   
D)  the line   
E)  the line

Question 14

Find the equation of the parabola with vertex (   , 3) and directrix

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Find the arclength of the curve   .

Accepted Answer

The answer of Find the arclength of the curve ...

Question 17

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...

Question 18

Find the value(s) of t for which the tangents to   is/are horizontal.

Accepted Answer

A)    
B)  0 
C)    
D)    
E)    
A)    
B)  0 
C)    
D)    
E)

Question 19

Sketch and identify the curve     for   by eliminating the parameter t and label the direction of increasing t.

Accepted Answer

cos t = x

Question 20

Express the given curve in polar coordinates.

Accepted Answer

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

Find the rectangular coordinates of the point whose polar coordinates are given.

State the name that describes the polar curve most precisely.

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at , and foci on .

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

Find the equation of the tangent to the curve and at .

State the definition of a parabola. Use your definition to derive the equation of the parabola whose focus is at F(3, 9) and directrix x = 1.

Put the rectangular equation y = 3x² + 3 into parametric form.

Find the arclength of the curve from to

Find the equation of the hyperbola with vertices and asymptotes .

Find the equation for the parabola whose directrix is y = 3 and vertex is at (-7, 2). Where is the focus located?

Find the arclength of the curve from to .

Find the equation for the given graph when A = 3.

If the tangent to the curve at the origin is

Find the equation of the parabola with vertex ( , 3) and directrix

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

Find the arclength of the curve .

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

Find the value(s) of t for which the tangents to is/are horizontal.

Sketch and identify the curve for by eliminating the parameter t and label the direction of increasing t.

Express the given curve in polar coordinates.

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

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Exam 10: Parametric and Polar Curves; Conic Sections

Find the rectangular coordinates of the point whose polar coordinates are given.

State the name that describes the polar curve most precisely.

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at , and foci on .

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

Find the equation of the tangent to the curve and at .

State the definition of a parabola. Use your definition to derive the equation of the parabola whose focus is at F(3, 9) and directrix x = 1.

Put the rectangular equation y = 3x2 + 3 into parametric form.

Find the arclength of the curve from to

Find the equation of the hyperbola with vertices and asymptotes .

Find the equation for the parabola whose directrix is y = 3 and vertex is at (-7, 2). Where is the focus located?

Find the arclength of the curve from to .

Find the equation for the given graph when A = 3.

If the tangent to the curve at the origin is

Find the equation of the parabola with vertex ( , 3) and directrix

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

Find the arclength of the curve .

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

Find the value(s) of t for which the tangents to is/are horizontal.

Sketch and identify the curve for by eliminating the parameter t and label the direction of increasing t.

Express the given curve in polar coordinates.

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

Put the rectangular equation y = 3x² + 3 into parametric form.