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Find the eccentricity and the distance from the pole to the directrix of the conic.

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Find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. use a graphing utility to confirm your results.

asked Feb 18, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The polar equation is .

Convert the equation into the conic form ,

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

Compare with .

Since , the equation represents an ellipse.

Step 2:

Graph the above polar equation using some polar coordinates.

Construct a table for different values of .

Graph:

Draw the polar coordinate plane.

Plot the  polar coordinates found in the table.

Connect the points with smooth curve.

Observe the graph: The ellipse eccentricity image and distance image.

Solution:

Eccentricity image.

Distance image.

answered Feb 24, 2015 by david Expert

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