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anyanavicka [17]
3 years ago
7

Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±11)

Mathematics
1 answer:
Katen [24]3 years ago
3 0

Answer:

\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1 is standard equation of hyperbola with vertices at (0, ±9) and foci at (0, ±11).

Step-by-step explanation:

We have given the vertices at (0, ±9) and foci at (0, ±11).

Let (0,±a)  = (0,±9) and (0,±c)  = (0,±11)

The standard equation of parabola is:

\frac{y^{2} }{a^{2} } -\frac{x^{2} }{b^{2} }=1

From statement, a  = 9

c² = a²+b²

(11)²  = (9)²+b²

121-81  = b²

40  = b²

Putting the value of a² and b² in standard equation of parabola, we have

\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1 which is the answer.

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