An ellipse has foci 4,2 , 2,2 and it passes through the point P 2,4 . The eccentricity of the ellipse is

Question

An ellipse has foci 4,2 , 2,2 and it passes through the point P 2,4 . The eccentricity of the ellipse is, t a n π 10, t a n π 12, t a n π 6, t a n π 8

MARKS App · Accepted Answer

Let, 4 , 2 = S 1 and 2 , 2 = S 2 and eccentricity of ellipse is e then S 1 S 2 = 2 a e and P S 1 + P S 2 = 2 a (where 2 a is length of major axis) ⇒ e = S 1 S 2 P S 1 + P S 2 = 2 2 2 + 2 ⇒ e = 1 2 + 1 = 2 - 1 = t a n π 8

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