An ellipse has OB as semi minor axis, F and F ′ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

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​ ∵ ∠ FBF ′ = 9 0 ∘ ∴ ( a 2 e 2 + b 2 ​ ) 2 + ( a 2 e 2 + b 2 ​ ) 2 = ( 2 a e ) 2 ⇒ 2 ( a 2 e 2 + b 2 ) = 4 a 2 e 2 ⇒ e 2 = b 2 / a 2 Also e 2 = 1 − b 2 / a 2 = 1 − e 2 ⇒ 2 e 2 = 1 , e = 2 ​ 1 ​ . ​

Mathematics - Ellipse Question with Solution | TestHub

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