Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus rectum of the hyperbola `16 x^2-9y^2=144`

Explanation

`16x^2- 9y^2=144`

`implies{16x^2}/144-{9 y^2}/144=1`

` implies {x^2}/9-{ y^2}/16=1`

Here,` a=3,b=4`

Eccentricity is,

`e=sqrt{1+{b^2}/a^2}`

`implies e=sqrt{1+16/9}=5/3`

Foci is,

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