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Question

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the hyperbola,

9y24x2=36

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Solution

The given equation of hyperbola is,
9y24x2=36
i.e.9y2364x236=1y24x29=1Which is of the formy2a2x2b2=1
The foci and vertices of the hyperbola lie on y - axis.
a2=4a=2 and b2=9b=3Nowc2=a2+b24+9=13c=13Coordinates of foci are(0,±c)i.e.(0,±13)Coordinats of vertices are(0,±a)i.e.(0,±2)Eccentricity(e)=ca=132Length fo latus rectum=2b2a=2×92=9.


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