8. (a) Write polar equations that represent a conic with eccentricity . For what values of is the conic an ellipse? a hyperbola? a parabola?
(b) What conic does the polar equation represent? Graph the conic.
The polar equations that represent a conic with eccentricity and values of for which conic is an ellipse, a hyperbola, and a parabola.
The polar equation of the conic has the form,
Here, is the eccentricity and is the distance from the directrix of conic.
The above equations represent an ellipse if eccentricity is equals to 1. It represents a hyperbola if and a parabola if eccentricity is greater than 1
The conic that the polar equation represents and graph of the conic.
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