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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 5y29x2=36

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Solution

The given equation is 5y29x2=36
y2(365)x24=1
y2(65)2x222=1...(1)
On comparing equation (1) with the standard equation of hyperbola
i.e., y2a2x2b2=1,
we obtain a=65 and b=2
We know that a2+b2=c2, where c=ae
c2=365+4=565
c=565=2145
Therefore, the coordinates of the foci are (0,±2145)
The coordinates of the vertices are (0,±65)
Eccentricity e= ca=(2145)(65)=143
Length of latus rectum = 2b2a=2×4(65)=453

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