21-24 Polar Equation for a Ellipse A polar equation of a conic is given (a) Show that the conic is a ellipse, and sketch its graph. (b) Find the vertex and directrix, and indicate them on the graph. (c) Find the center of the ellipse and the length of the major and minor axes.
The conic is an ellipse and the graph of the conic.
The polar equation of the given conic is,
The standard equation of the conic is,
Here, is the eccentricity of the conic, is the distance of directrix from the focus, and are the polar coordinates.
The equation represents a parabola if , an ellipse if , and a hyperbola if .
Divide the denominator and the nominator of equation by .
The vertices and the directrix of the conic.
The center of the ellipse and the length of the major and the minor axes.
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