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.
Text Solution
Verified by Experts
(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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