17-20 Polar Equation for a parabola A polar equation of a conic is given (a) Show that the conic is a parabola, and sketch its graph. (b) Find the vertex and directrix, and indicate them in the graph.
The conic is a parabola 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 vertex and directrix of the conic.
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