Question

$\Large{\underline{\underline{\bf{Question:-}}}}$
Vertices (0, ±5), foci (0, ±8)​

Answer 1

$\underline{\underline{\huge{\pink{\tt{\textbf Answer :-}}}}}$

We need to find equation of hyperbole

Given

Vertices (0, ±5)

Foci (0, ±8)

Since vertices are on the y-axis

So required equation of hyperbole is

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

we know that

Vertices= (0, ±a)

Given vertices=(0, ±5)

so,a=5

${a}^{2} = 25$

Foci are (0, ±c)

given Foci are (0, ±8)

so,c=8

Axis of hyperbole is y-axis

${c}^{2} = {a}^{2} + {b}^{2}$

${(8)}^{2} = {(5)}^{2} + {b}^{2}$

${b}^{2} = 64 - 25$

${b}^{2} = 39$

Required equation of hyperbole is

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

Putting values:

$\frac{ {y}^{2} }{25} - \frac{ {x}^{2} }{39} = 1$

Hope it will helps you ❤️

Answer 2

Answer:

answer is in attachment I hope it will help you...