21-28 ■ Graphing Shifted Hyperbolas An equation of hyperbola is given. (a) Find the centre, vertices, foci, and asymptotes of the hyperbola. (b) Sketch a graph showing the hyperbola and its asymptotes.
The center, vertices, foci, and asymptotes of the given hyperbola.
An equation of hyperbola
Completing the square of given equation, we get the equation of shifted hyperbola, then comparing the equation of given hyperbola with equation of shifted hyperbola,
Rearranging equation of hyperbola, we get
The shifted hyperbola has center, and has a horizontal transverse axis.
Its graph will have similar shape as the unshifted hyperbola
Since and , we get , , and
A graph showing the hyperbola and its asymptotes.
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