Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus rectum of the hyperbola `4x^2-3y^2=36`

Explanation

`4x^2-3 y^2=36`

`implies{x^2}/9-{ y^2}/12=1`

Here,` a=3,b=sqrt{12}`

Eccentricity is,

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

`implies e=sqrt{1+12/9}=sqrt{21}/3`

Foci is,

`(pm a e,0)=(pm3 xxsqrt21 /3,0)=(pm sqrt21,0)`

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