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Question

Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola 9y24x2=36

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Solution

The given equation is 9y24x2=36
It can be written as
9y24x2=36
y24x29=1
y222x232=1...(1)
On comparing equation (1) with the standard equation of hyperbola
i.e., y2a2x2b2=1
we obtain a=2 and b=3
We know that a2+b2=c2, where c=ae
c2=4+9=13
c=13
Therefore, the coordinates of the foci are (0,±13)
The coordinates of the vertices are (0,±2)
Eccentricity e =ca=132
Length of latus rectum = 2b2a=2×92=9

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