College Algebra 6/e   Barnett/Ziegler/Byleen
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Chapter 9: Additional Topics in Analytic Geometry

Worked Exercises

Chapter 9: Additional Topics in Analytic Geometry

Graph the equation, and locate the focus and directrix.

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Find the equation of the parabola having its vertex at the origin, its axis as indicated, and passing through the indicated point.

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Use the definition of a parabola and the distance formula to find the equation of a parabola with:

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Sketch a graph of the equation, find the coordinates of the focus and the length of the major and minor axes.

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Find the equation of the ellipse in the form
if the center is at the origin, and:

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Sketch a graph of the equation, find the coordinates of the focus, and find the length of the transverse and conjugate axes.

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Find the equation of the hyperbola in the form
if the center is at the origin, and:

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(A) Find translation formula that translate the origin to the indicated point (h, k).
(B) Write the equation of the curve for the translated system.
(C) Identify the curve.

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(A) Write the equation in one of the standard forms listed in Table 1.
(B) Identify the curve.

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Use the given information to find the equation of the conic. Express the answer in the form Ax² + Cy² + Dx + Ey + F = 0 with integer coefficients A > 0.

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Plot the plane curve by use of a table of values (see Example 1). Obtain an equation of x and y by eliminating the parameter, and identify the curve. The interval for the parameter is the whole real line).

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Obtain the equation in x and y by eliminating the parameter. Use the simpler of the two forms to plot the curve. Name the curve if it is a curve we have identified.

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