find the equation of hyperabola where foci are (0,12) and (0,-12)and the length of the latus rectum is 36

Explanation

Here, Foci of hyperbola `= (0,+-12)`

That means the transverse axis of the hyperbola is `Y`-axis.

So, the equation will be of the type,

`y^2/a^2-x^2/b^2 = 1->(1)`

Also, `c = 12`

Length of latus rectum ` = 36`

`:. 2b^2/a = 36=> b^2 = 18a`

In a hyperbola, `c^2 = a^2+b^2`

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