What are the standard equations for lines and conic sections in polar coordinates? Give examples.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.2: The Ellipse
Problem 69E
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What are the standard equations for lines and conic sections in polar coordinates? Give examples.

Expert Solution
Step 1

The standard polar equation for lines is given by

Calculus homework question answer, step 1, image 1
Step 2

For example:

If (4, 450) is the foot of the perpendicular, then the polar equation of the line is

Calculus homework question answer, step 2, image 1
Step 3

The standard polar equation for a conic with eccentricity (e) and directrix x = k and focus at the (0, 0) is given by

Calculus homework question answer, step 3, image 1
Step 4

For example:

The polar equation for a conic with eccentricity (e = 1) and directrix x = 5 is

Calculus homework question answer, step 4, image 1
Step 5

The standard polar equation for a conic with eccentricity (e) and directrix x = - k and focus at the (0, 0) is given by

Calculus homework question answer, step 5, image 1
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