Question 1

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

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Question 2

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

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Question 3

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

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Question 4

Sketch the graph of the ellipse, showing the foci .

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Question 5

Lissajous figures are used in the study of electrical circuits to determine the phase difference   between a known voltage   and an unknown voltage   having the same frequency. The voltages are graphed parametrically as   and   . If   is acute, then   where y int  is the nonnegative y -intercept and y max  is the maximum y -value on the curve. Graph the parametric curve and use the graph to approximate   in degrees if

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Question 6

Find an equation for the parabola that has a horizontal axis and passes through the given points.

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Question 7

Find an equation for the parabola shown in the figure.

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Question 8

Find the eccentricity.

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Question 9

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

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Question 10

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

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Question 11

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

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Question 12

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

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Question 13

Sketch the graph of the polar equation

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Question 14

Find an equation for the indicated half of the parabola.

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Question 15

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.

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Question 16

Classify the conic.

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

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Question 19

Find the foci of the ellipse.

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Question 20

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

Accepted Answer

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

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

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

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

Sketch the graph of the ellipse, showing the foci .

Find an equation for the parabola that has a horizontal axis and passes through the given points.

Find an equation for the parabola shown in the figure.

Find the eccentricity.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

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

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

Sketch the graph of the polar equation

Find an equation for the indicated half of the parabola.

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.

Classify the conic.

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

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

Find the foci of the ellipse.

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

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

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

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

Sketch the graph of the ellipse, showing the foci .

Find an equation for the parabola that has a horizontal axis and passes through the given points.

Find an equation for the parabola shown in the figure.

Find the eccentricity.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

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

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

Sketch the graph of the polar equation

Find an equation for the indicated half of the parabola.

Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.

Classify the conic.

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

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

Find the foci of the ellipse.

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

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