Question

Identify the conic and sketch its graph.

Answer 1

Step 1:

The polar equation .

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

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

Divide numarator and denominator by 2.

Compare with .

Since , the equation represents an ellipse.

Step 2:

Graph the above polar equation using some polar coordinates.

For  ,

For ,

For ,

For ,

For ,

For ,

Answer 2

Contd...

Construct a table for a different values of .

Step 3:

Graph:

Draw the polar coordinate plane.

Plot the  polar coordinates found in the table.

Connect the points with smooth curve.

Observe the graph: The polar equation is ellipse.

Solution:

The conic is ellipse.

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