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Maths-

General

Easy

Question

If the eccentricities of the hyperbolas $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ and $fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction minus fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction equals 1$ be e and $e subscript 1 end subscript$ , then $fraction numerator 1 over denominator e to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator e subscript 1 end subscript superscript 2 end superscript end fraction equals$

1
2
3
None of these

The correct answer is: 1

$e equals square root of 1 plus fraction numerator b to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction end root$ Þ $e to the power of 2 end exponent equals fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction$
$e subscript 1 end subscript equals square root of 1 plus fraction numerator a to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction end root$ Þ $e subscript 1 end subscript superscript 2 end superscript equals fraction numerator b to the power of 2 end exponent plus a to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction$ Þ $fraction numerator 1 over denominator e subscript 1 end subscript superscript 2 end superscript end fraction plus fraction numerator 1 over denominator e to the power of 2 end exponent end fraction equals 1$ .

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