In each of the following find the equations of the hyperbola satisfying the given condition: foci `(0,+-12)` latus rectum`=36`

Explanation

We have given foci `(0,+-12)` and latus rectum=36

Hence, `(2a^2)/b=36`

`implies a^2=18b`

Here the foci are on the x-axis .

Therefore, the equation of the hyperbola is of the form

`y^2/a^2− a^2/b^2=1`

Since the foci are `(0,+-12),c=be=+-12`.

We know that
`a^2+b^2=c^2`

...