Question 1

Find the standard form of the parabola with the given characteristics.focus: (2, 9) vertex: (2, 4)

Accepted Answer

A) (x - 2)2 = 20(y - 4) 
B) (x + 2)2 = 20(y + 4) 
C) (x - 4)2 = 20(y - 2) 
D) (x + 4)2 = 20(y + 2) 
E) (x + 2)2 = 5(y + 4) 
A) (x - 2)2 = 20(y - 4) 
B) (x + 2)2 = 20(y + 4) 
C) (x - 4)2 = 20(y - 2) 
D) (x + 4)2 = 20(y + 2) 
E) (x + 2)2 = 5(y + 4)

Question 2

Find the vertex and focus of the parabola.

Accepted Answer

A) vertex:   focus: (0, 0) 
B) vertex:   focus: (0, 0) 
C) vertex: (0, 0) focus:   
D) vertex: (0, 0) focus:   
E) vertex: (0, 0) focus:   
A) vertex:   focus: (0, 0) 
B) vertex:   focus: (0, 0) 
C) vertex: (0, 0) focus:   
D) vertex: (0, 0) focus:   
E) vertex: (0, 0) focus:

Question 3

Find the center and foci of the hyperbola.

Accepted Answer

A) center: (8, -4) foci: (8, -10), (8, 2) 
B) center: (-8, 4) foci: (-8, -2), (-8, 10) 
C) center: (4, -8) foci: (-2, -8), (10, -8) 
D) center: (-8, 4) foci: (-14, 4), (-2, 4) 
E) center: (-4, 8) foci: (-4, 2), (-4, 14) 
A) center: (8, -4) foci: (8, -10), (8, 2) 
B) center: (-8, 4) foci: (-8, -2), (-8, 10) 
C) center: (4, -8) foci: (-2, -8), (10, -8) 
D) center: (-8, 4) foci: (-14, 4), (-2, 4) 
E) center: (-4, 8) foci: (-4, 2), (-4, 14)

Question 4

Find any zeros of r on the interval   .

Accepted Answer

A) zeros:   
B) zeros:   
C) zeros:   
D) zeros:   
E) zeros:   
A) zeros:   
B) zeros:   
C) zeros:   
D) zeros:   
E) zeros:

Question 5

Find a polar equation of the conic with the given characteristics and with one focus at the pole.Conic Eccentricity DirectrixEllipse

Accepted Answer

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

Question 6

If a new comet were discovered with an eccentricity of   and whose length of the major axis of orbit is approximately 6.46 astronomical units, how close would the comet come to the sun (perihelion distance)? The perihelion distance is defined by the equation   . Round answer to three decimal places, if necessary.

Accepted Answer

A) approximately 2.778 astronomical units 
B) approximately 1.389 astronomical units 
C) approximately 3.682 astronomical units 
D) approximately 1.841 astronomical units 
E) approximately 1.14 astronomical units 
A) approximately 2.778 astronomical units 
B) approximately 1.389 astronomical units 
C) approximately 3.682 astronomical units 
D) approximately 1.841 astronomical units 
E) approximately 1.14 astronomical units

Question 7

Match the graph to a set of parametric equations.

Accepted Answer

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

Question 8

Match the graph with its equation.

Accepted Answer

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

Question 9

Identify the conic and sketch its graph.   Use either grid below for your graph, whichever is more convenient.

Accepted Answer

The answer of Identify the conic and sketch its graph....

Question 10

Find the standard form of the equation of the hyperbola with the given characteristics.vertices: (5, 0), (5, 4) foci: (5, -1), (5, 5)

Accepted Answer

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

Question 11

Find the standard form of the equation of the ellipse with the following characteristics.foci:   major axis of length: 20

Accepted Answer

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

Question 12

Identify the type of polar graph.

Accepted Answer

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

Question 13

Match the graph with its equation.

Accepted Answer

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

Question 14

Which answer is a rectangular form of the given polar equation?

Accepted Answer

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

Question 15

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places if necessary.

Accepted Answer

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

Question 16

Find the standard form of the parabola with the given characteristic and vertex at the origin.vertical axis and passes through point

Accepted Answer

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

Question 17

Find the standard form or the equation of the ellipse with vertices (F1F1F1S1F1F1F107, 0) and eccentricity   .

Accepted Answer

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

Question 18

Sketch the graph of the polar equation using symmetry, zeros, maximum r-values and any other additional points.   Use either grid below for your graph, whichever is more convenient.

Accepted Answer

The answer of Sketch the graph of the polar equation...

Question 19

Find a polar equation of the conic with the given characteristics and with one focus at the pole.Conic VerticesEllipse

Accepted Answer

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

Question 20

Test for symmetry with respect to F1F1F1S1F1F1F10 = F1F1F1S1F1F1F10/2, the polar axis, and the pole.

Accepted Answer

A) symmetric with respect to the pole 
B) symmetric with respect to the polar axis 
C) symmetric with respect to F1F1F1S1F1F1F10 = F1F1F1S1F1F1F10/2 
D) symmetric with respect to the pole and the polar axis 
E) symmetric with respect to the pole and F1F1F1S1F1F1F10 = F1F1F1S1F1F1F10/2 
A) symmetric with respect to the pole 
B) symmetric with respect to the polar axis 
C) symmetric with respect to F1F1F1S1F1F1F10 = F1F1F1S1F1F1F10/2 
D) symmetric with respect to the pole and the polar axis 
E) symmetric with respect to the pole and F1F1F1S1F1F1F10 = F1F1F1S1F1F1F10/2

Find the standard form of the parabola with the given characteristics.focus: (2, 9) vertex: (2, 4)

Find the vertex and focus of the parabola.

Find the center and foci of the hyperbola.

Find any zeros of r on the interval .

Find a polar equation of the conic with the given characteristics and with one focus at the pole.Conic Eccentricity DirectrixEllipse

Match the graph to a set of parametric equations.

Match the graph with its equation.

Identify the conic and sketch its graph. Use either grid below for your graph, whichever is more convenient.

Find the standard form of the equation of the hyperbola with the given characteristics.vertices: (5, 0), (5, 4) foci: (5, -1), (5, 5)

Find the standard form of the equation of the ellipse with the following characteristics.foci: major axis of length: 20

Identify the type of polar graph.

Match the graph with its equation.

Which answer is a rectangular form of the given polar equation?

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places if necessary.

Find the standard form of the parabola with the given characteristic and vertex at the origin.vertical axis and passes through point

Find the standard form or the equation of the ellipse with vertices (7, 0) and eccentricity .

Sketch the graph of the polar equation using symmetry, zeros, maximum r-values and any other additional points. Use either grid below for your graph, whichever is more convenient.

Find a polar equation of the conic with the given characteristics and with one focus at the pole.Conic VerticesEllipse

Test for symmetry with respect to  = /2, the polar axis, and the pole.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Additional Topics in Trigonometry

Filters

Exam 13: Topics in Analytic Geometry

Find the standard form of the parabola with the given characteristics.focus: (2, 9) vertex: (2, 4)

Find the vertex and focus of the parabola.

Find the center and foci of the hyperbola.

Find any zeros of r on the interval .

Find a polar equation of the conic with the given characteristics and with one focus at the pole.Conic Eccentricity DirectrixEllipse

Match the graph to a set of parametric equations.

Match the graph with its equation.

Identify the conic and sketch its graph. Use either grid below for your graph, whichever is more convenient.

Find the standard form of the equation of the hyperbola with the given characteristics.vertices: (5, 0), (5, 4) foci: (5, -1), (5, 5)

Find the standard form of the equation of the ellipse with the following characteristics.foci: major axis of length: 20

Identify the type of polar graph.

Match the graph with its equation.

Which answer is a rectangular form of the given polar equation?

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places if necessary.

Find the standard form of the parabola with the given characteristic and vertex at the origin.vertical axis and passes through point

Find the standard form or the equation of the ellipse with vertices (7, 0) and eccentricity .

Sketch the graph of the polar equation using symmetry, zeros, maximum r-values and any other additional points. Use either grid below for your graph, whichever is more convenient.

Find a polar equation of the conic with the given characteristics and with one focus at the pole.Conic VerticesEllipse

Test for symmetry with respect to  = /2, the polar axis, and the pole.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Additional Topics in Trigonometry

Filters