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
Compare the equation of given hyperbola with equation of shifted hyperbola,
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 . Thus the foci will lie units to the right and to the left of the center, and the vertices will lie 3 units to either side of the centre.
A graph showing the hyperbola and its asymptotes.
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