25-28 Polar Equation for a Hyperbola A polar equation of a conic is given.(a) Show that the conic is a hyperbola, and sketch its graph. (b) Find the vertices and directrix, and indicate them on the graph.(c) Find the center of the hyperbola, and sketch the asymptotes.
The given polar equation is a hyperbola. Also draw the graph of it.
The given polar equation is,
The general equation of conic in polar form with one focus at origin and eccentricity is given by as below.
The conditions for different conic section for above formula follows as below.
a) It is a parabola if .
b) It is an ellipse if .
c) It is hyperbola .
Consider the given equation,
Compare above equation with general equation of a conic for eccentricity
The vertices and directrix of hyperbola and show them on the graph.
The center and asymptotes of hyperbola and show it on the graph.
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