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Question

Find the equation of the hyperbola satisfying the given conditions: Foci (±35,0) the latus rectum is of length 8

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Solution

Here the foci are on the x-axis
Therefore, the equation of the hyperbola is of the form x2a2y2b2=1
Since the foci are (±35,0)ae=c=±35
Length of latus rectum =8
2b2a=8
b2=4a
We know that a2+b2=c2
a2+4a=45
a2+4a45=0
a2+9a5a45=0
(a+9)(a5)=0
a=9,5
Since a in non-negative a=5
b2=4a=4×5=20
Thus the equation of the hyperbola is x225y220=1

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