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Question

If e and e be the eccentricities of a hyperbola and its conjugate, then 1e2+1e2 is equal to.

A
0
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B
1
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C
2
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D
None of these
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Solution

The correct option is C 1
Equation of hyperbola is x2a2y2b2=1
b2=a2(e21)
e2=1+b2a2=a2+b2a2
Equation of conjugate hyperbola is
x2a2y2b2=1
y2b2x2a2=1
e2=1+a2b2=a2+b2b2
Now, 1e2+1e2=a2+b2a2+b2=1

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