For the following hyperbolas find the lengths of transverse and conjugate axes, eccentricity and coordinates of foci and vertices, length of the latus-rectum, equations of the directrices: `6x^2-9y^2=144` `3x^2-6y^2=-18`

Explanation

The equation `16x^2−9y^2=144`
can be written as` (x^2)/9​−(y^2)/16​=−1`


This is of the form `(x^2)/(a^2)​−(y^2)/(b^2)​=−1`
.
so,`a^2=9,b^2=16⇒a=3,b=4`


The length of transverse axis = 2b = 8


The length of conjugate axis = 2a =6

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