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Use a graphing utility to graph the polar equation. Identify the graph and find its eccentricity.

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Use a graphing utility to graph the polar equation. Identify the graph and find its eccentricity.

asked Feb 18, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The polar equation image.

Graph the above polar equation using some polar coordinates.

Construct a table for different values of .

image image
image image
image

Graph:

Draw the polar coordinate plane.

Plot the  polar coordinates found in the table.

Connect the points with smooth curve.

Step 2:

The polar equation image.

To identify the type of conic, rewrite the equation in the form image.

where image is the eccentricity and image is the distance between the focus(pole) and the directrix.

image

Compare with image

image

Since image, the equation represents a parabola.

Solution:

image represents a parabola.

Eccentricity image.

answered Feb 24, 2015 by david Expert

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