55-64 ■ Find the Equation of the Conic Find an equation for the conic section with the given properties.
58. The hyperbola with vertices and asymptotes .
An equation for the hyperbola with vertices , and asymptotes .
The vertices and asymptotes of a hyperbola are and .
Standard equation of the hyperbola is , having center and asymptotes are .
The vertices of a hyperbola are , vertices are lying on -axis and center is the midpoint of the vertices, so the center is . The axis of hyperbola is along the -axis, so it is a up and down hypebola. For a up and down hyperbola having center at origin, the asymptotes are as follows,
Compare the given equation of asymptotes with above equation, so . The distance between vertex and center is the value of , so , and
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