If the circle whose diameter is the major axis of the ellipse x 2 a 2 + y 2 b 2 = 1 a b 0 meets the minor axis at point P and the orthocentre of ∆ P F 1 F 2 lies on the ellipse, where F 1 and F 2 are the foci of the ellipse, then the square of the eccentricity of the ellipse is

Question

If the circle whose diameter is the major axis of the ellipse x 2 a 2 + y 2 b 2 = 1 a > b > 0 meets the minor axis at point P and the orthocentre of ∆ P F 1 F 2 lies on the ellipse, where F 1 and F 2 are the foci of the ellipse, then the square of the eccentricity of the ellipse is, 5 - 1 2, 3 - 1, 1 2, 3 2

MARKS App · Accepted Answer

m F 1 B ⋅ m P F 2 = − 1 ⇒ a - 0 0 - a e × b - 0 0 - - a e = - 1 ⇒ b 2 a 2 = e 2 ⇒ e 4 + e 2 − 1 = 0 ∴ e 2 = 5 - 1 2

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