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If the latus rectum subtends a right ang...

If the latus rectum subtends a right angle at the center of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , then find its eccentricity.

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(1) In the figure, latus rectum PQ subtends right angle at the centre of the hyperbola.
(2) `therefore" "OS=SP`
(3) `rArr" "ae=(b^(2))/(a)`
(4) `rArr" "e=(b^(2))/(a^(2))=e^(2)-1`
(5) `rArr" "e^(2)-e-1=0`
(6) `rArr" "e=(1+sqrt5)/(2)`
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