Question 1

Which set of parametric equations represents the following line or conic?Use   and   .Line: passes through

Accepted Answer

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

Question 2

Find the standard form of the parabola with the given characteristics.directrix: x = 9 vertex: (4, 6)

Accepted Answer

A) (x + 4)2 = -20(y + 6) 
B) (x - 4)2 = -20(y - 6) 
C) (x + 6)2 = -20(y + 4) 
D) (y + 6)2 = -20(x + 4) 
E) (y - 6)2 = -20(x - 4) 
A) (x + 4)2 = -20(y + 6) 
B) (x - 4)2 = -20(y - 6) 
C) (x + 6)2 = -20(y + 4) 
D) (y + 6)2 = -20(x + 4) 
E) (y - 6)2 = -20(x - 4) E

Question 3

Analyze the curves below and determine the way(s) the plane curves differ from each other. Make use of sketchs of the graphs to aid in your analysis.

Accepted Answer

Answers may vary.Curve (a) Curve (b)

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.6x2 - y2 - 8x + y + 8 = 0

Accepted Answer

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

Question 7

Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote.Name of Graph Polar Equation AsymptoteStrophoid     Use either grid below for your graph, whichever is more convenient.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 8

Which set of parametric equations represents the graph of the following rectangular equation using   ?

Accepted Answer

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

Question 9

Find an interval for F1F1F1S1F1F1F10 for which the graph is traced only once.

Accepted Answer

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

Question 10

Find the standard form of the equation of the hyperbola with the given characteristics.vertices: (0, F1F1F1S1F1F1F102) foci: (0, F1F1F1S1F1F1F108)

Accepted Answer

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

Question 11

Find the standard form of the parabola with the given characteristic and vertex at the origin.directrix: x = 8

Accepted Answer

A) x2 = -32y 
B) x2 = 32y 
C) x2 = 8y 
D) y2 = 8x 
E) y2 = -32x 
A) x2 = -32y 
B) x2 = 32y 
C) x2 = 8y 
D) y2 = 8x 
E) y2 = -32x

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Question 15

Use a graphing utility to graph the polar equation. Describe the resulting graph.

Accepted Answer

A) rose curve with 5 petals, rotated 5 radians 
B) rose curve with 5 petals, rotated 3 radians 
C) lemniscate rotated 3 radians 
D) limaçon rotated 3 radians 
E) cardioid rotated 5 radians 
A) rose curve with 5 petals, rotated 5 radians 
B) rose curve with 5 petals, rotated 3 radians 
C) lemniscate rotated 3 radians 
D) limaçon rotated 3 radians 
E) cardioid rotated 5 radians

Question 16

Which set of parametric equations represents the following line or conic?Use   and   .Ellipse: vertices   ,foci

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

A projectile is launched from ground level at an angle of F1F1F1S1F1F1F10 with the horizontal. The initial velocity is   feet per second and the path of the projectile is modeled by the parametric equations   and   .Use a graphing utility to graph the paths of a projectile launched from ground level with the values given for F1F1F1S1F1F1F10 and   . Use the graph to approximate the maximum height and range of the projectile to the nearest foot.   ,

Accepted Answer

A) maximum height F1F1F1S1F1F1F10 100 feet range F1F1F1S1F1F1F10 9 feet 
B) maximum height F1F1F1S1F1F1F10 9 feet range F1F1F1S1F1F1F10 100 feet 
C) maximum height F1F1F1S1F1F1F10 67 feet range F1F1F1S1F1F1F10 188 feet 
D) maximum height F1F1F1S1F1F1F10 188 feet range F1F1F1S1F1F1F10 67 feet 
E) maximum height F1F1F1S1F1F1F10 43 feet range F1F1F1S1F1F1F10 8 feet 
A) maximum height F1F1F1S1F1F1F10 100 feet range F1F1F1S1F1F1F10 9 feet 
B) maximum height F1F1F1S1F1F1F10 9 feet range F1F1F1S1F1F1F10 100 feet 
C) maximum height F1F1F1S1F1F1F10 67 feet range F1F1F1S1F1F1F10 188 feet 
D) maximum height F1F1F1S1F1F1F10 188 feet range F1F1F1S1F1F1F10 67 feet 
E) maximum height F1F1F1S1F1F1F10 43 feet range F1F1F1S1F1F1F10 8 feet

Question 19

Find the standard form of the parabola with the given characteristic and vertex at the origin.focus: (0, 9)

Accepted Answer

A) x2 = 36y 
B) x2 = 9y 
C) x2 = -9y 
D) y2 = 36x 
E) y2 = 9x 
A) x2 = 36y 
B) x2 = 9y 
C) x2 = -9y 
D) y2 = 36x 
E) y2 = 9x

Question 20

Find the maximum value of   on the interval   .

Accepted Answer

A) maximum value of   : r = 25 where   
B) maximum value of   : r = 25 where   
C) maximum value of   : r = 5 where   
D) maximum value of   : r = 5 where   
E) maximum value of   : r = 5 where   
A) maximum value of   : r = 25 where   
B) maximum value of   : r = 25 where   
C) maximum value of   : r = 5 where   
D) maximum value of   : r = 5 where   
E) maximum value of   : r = 5 where

Which set of parametric equations represents the following line or conic?Use and .Line: passes through

Find the standard form of the parabola with the given characteristics.directrix: x = 9 vertex: (4, 6)

Analyze the curves below and determine the way(s) the plane curves differ from each other. Make use of sketchs of the graphs to aid in your analysis.

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

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

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.6x² - y² - 8x + y + 8 = 0

Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote.Name of Graph Polar Equation AsymptoteStrophoid Use either grid below for your graph, whichever is more convenient.

Which set of parametric equations represents the graph of the following rectangular equation using ?

Find an interval for  for which the graph is traced only once.

Find the standard form of the equation of the hyperbola with the given characteristics.vertices: (0, 2) foci: (0, 8)

Find the standard form of the parabola with the given characteristic and vertex at the origin.directrix: x = 8

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

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

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

Use a graphing utility to graph the polar equation. Describe the resulting graph.

Which set of parametric equations represents the following line or conic?Use and .Ellipse: vertices ,foci

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

Find the standard form of the parabola with the given characteristic and vertex at the origin.focus: (0, 9)

Find the maximum value of on the interval .

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

Which set of parametric equations represents the following line or conic?Use and .Line: passes through

Find the standard form of the parabola with the given characteristics.directrix: x = 9 vertex: (4, 6)

Analyze the curves below and determine the way(s) the plane curves differ from each other. Make use of sketchs of the graphs to aid in your analysis.

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

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

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.6x2 - y2 - 8x + y + 8 = 0

Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote.Name of Graph Polar Equation AsymptoteStrophoid Use either grid below for your graph, whichever is more convenient.

Which set of parametric equations represents the graph of the following rectangular equation using ?

Find an interval for  for which the graph is traced only once.

Find the standard form of the equation of the hyperbola with the given characteristics.vertices: (0, 2) foci: (0, 8)

Find the standard form of the parabola with the given characteristic and vertex at the origin.directrix: x = 8

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

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

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

Use a graphing utility to graph the polar equation. Describe the resulting graph.

Which set of parametric equations represents the following line or conic?Use and .Ellipse: vertices ,foci

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

Find the standard form of the parabola with the given characteristic and vertex at the origin.focus: (0, 9)

Find the maximum value of on the interval .

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

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.6x² - y² - 8x + y + 8 = 0