Find the equations of the hyperbola satisfying the given conditions :Foci `(+-4,0)`, the latus rectum is of length 12

Explanation

Here, Foci of hyperbola `= (+-4,0)`

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

So, the equation will be of the type,

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

Also, `c = 4`

Length of latus rectum ` = 12`

`:. 2b^2/a = 12=> b^2 = 6a`

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

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