Find an equation of the hyperbola satisfying the indicated properties. Vertices at (0, 1) and (0, −1). asymptotes are the lines x=±3y

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Find an equation of the hyperbola satisfying the indicated properties.  Vertices at (0, 1) and (0, −1). asymptotes are the lines x=±3y

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Step 1  Observe that only y-coordinate of vertices is changing, thus we must have an up-down hyperbola whose standard equation is given by:  y2a2−x2b2=1  Step 2  Also note that in the case of up-down hyperbola, we have vertices (0, a) and (0, −a), thus comparing with the given vertices (0, 1) and (0, −1), we have  a=1  Step 3  Next recall that in this case, equation of the asymptotes is given by x=±bay, comparing this with the given asymptotes x=±3y, we get  b=3  Step 4  Finally we plug the value a=1 and b=3 in the standard form of hyperbola to get the required equation as shown:  y212−x232=1  y2−x29=1  Answer:  y2−x29=1

Find an equation of the hyperbola satisfying the indicated properties. Vertices at

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