Question 1

Find an equation for the set of points in an xy-plane such that the sum of the distances from   and   is   .

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Question 2

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C.   -1   t   1

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Question 3

Find a polar equation in r and   of the parabola with focus at the pole and the given vertex.

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Question 4

Find an equation of the parabola that satisfies the condition. Vertex   , focus

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Question 5

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r per  is the perihelion distance measured in AU. The orbit of Saturn has r per  = 9.006 and e = 0.056. The motion of Encke's Comet has r per  = 0.3317 and e = 2.718282. Graph both the motion of the comet and the orbit of Saturn.

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Question 6

Sketch the graph of the polar equation.

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Question 7

Find an equation in x and y for the polar equation.

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Question 8

Find an equation for the ellipse shown in the figure.

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Question 9

Find an equation for the indicated half of the parabola.

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Question 10

Find an equation in x and y for the polar equation.

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Question 11

Find an equation of the parabola that satisfies the given conditions. Vertex at the origin, symmetric to the y-axis, and passing through the point ( 2, 5 )

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Question 12

Find an equation in x and y whose graph contains the points on the curve C.

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Question 13

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.

Accepted Answer

A) Hyperbola 
B) Circle 
C) Parabola with horizontal axis 
D) Ellipse 
E) Parabola with vertical axis 
A) Hyperbola 
B) Circle 
C) Parabola with horizontal axis 
D) Ellipse 
E) Parabola with vertical axis

Question 14

Find an equation in x and y that has the same graph as the polar equation.

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Question 15

Find an equation in x and y whose graph contains the points on the curve C.

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Question 16

Find an equation for the parabola shown in the figure.

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Question 17

Classify the conic.

Accepted Answer

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

Question 18

Find an equation in x and y for the polar equation.

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Question 19

Find a parametrization that gives the same graph as the given equation.

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Question 20

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.

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Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.

Find an equation of the parabola that satisfies the condition. Vertex , focus

Sketch the graph of the polar equation.

Find an equation in x and y for the polar equation.

Find an equation for the ellipse shown in the figure.

Find an equation for the indicated half of the parabola.

Find an equation in x and y for the polar equation.

Find an equation of the parabola that satisfies the given conditions. Vertex at the origin, symmetric to the y-axis, and passing through the point ( 2, 5 )

Find an equation in x and y whose graph contains the points on the curve C.

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.

Find an equation in x and y that has the same graph as the polar equation.

Find an equation in x and y whose graph contains the points on the curve C.

Find an equation for the parabola shown in the figure.

Classify the conic.

Find an equation in x and y for the polar equation.

Find a parametrization that gives the same graph as the given equation.

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

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Exam 11: Topics From Analytic Geometry

Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.

Find an equation of the parabola that satisfies the condition. Vertex , focus

Sketch the graph of the polar equation.

Find an equation in x and y for the polar equation.

Find an equation for the ellipse shown in the figure.

Find an equation for the indicated half of the parabola.

Find an equation in x and y for the polar equation.

Find an equation of the parabola that satisfies the given conditions. Vertex at the origin, symmetric to the y-axis, and passing through the point ( 2, 5 )

Find an equation in x and y whose graph contains the points on the curve C.

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.

Find an equation in x and y that has the same graph as the polar equation.

Find an equation in x and y whose graph contains the points on the curve C.

Find an equation for the parabola shown in the figure.

Classify the conic.

Find an equation in x and y for the polar equation.

Find a parametrization that gives the same graph as the given equation.

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Filters