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  • The equation of the hyperbola with vertices at (0, ± 6) and eccentricity 5/3 is ________ and its foci are __________ .

The equation of the hyperbola with vertices at (0, ± 6) and eccentricity 5/3 is ________ and its foci are __________ .

Answers (1)

Let the equation of parabola be \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1

b=6

e=5/3

a2=b2(e2-1)

a2=64

\frac{x^{2}}{64}-\frac{y^{2}}{36}=-1

\text { foci }=(0, \pm b e) \equiv\left(0, \pm \frac{5}{3} \times 6\right)=(0,\pm 10)

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