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Grade 12Algebra

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 ?

Profile image of sudhanshu
12 Years agoGrade 12
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1 Answer

Profile image of SHAIK AASIF AHAMED
12 Years ago
Hello student,
240-1005_Capture3.PNG
∵∠FBF′ = 90
∴ (sqrt(a2e2 + b2))2+(sqrt(a2e2+ b2))2 = (2ae)2
⇒ 2(a2e2+ b2)= 4a2e2
⇒ e2 = b2/a2
Also e2= 1- b2/a2 = 1 – e2
B(0, b)
F′(-ae, 0) O F(ae, 0)
2e2= 1,so e=1/\sqrt{2}
Thanks and Regards
Shaik Aasif
askIITians faculty

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