The graph of a polar equation of the form is a conic, where e > 0 is the eccentricity and | d | is the distance between the focus at the pole and its corresponding directrix.

The conic section equation is .

To determine the type of conic, rewrite the equation as

Divide numerator and denominator by 10.

Therefore, .

Since e = 1/2 (0 < e < 1), the conic section is ellipse. Sketch the upper half of the ellipse by plotting points from , as shown in figure. Then, using symmetry with respect to the polar axis, sketch the lower half.

For the ellipse in figure, the major axis is horizontal and the vertices lie at . So, the length of the major axis is . To find the length of the minor axis, can use the equation e = c / a and .