Variable ellipses are drawn with x = - 4 as directrix and the origin as the corresponding focus. The eccentricity of the locus of the extremities of the minor axes of these ellipses is

Question

Variable ellipses are drawn with x = - 4 as directrix and the origin as the corresponding focus. The eccentricity of the locus of the extremities of the minor axes of these ellipses is, 1, 2, 2, 1 2

MARKS App · Accepted Answer

Now k = b and h = a e Also a e - a e = 4 ⇒ a 1 - e 2 = 4 e ⇒ a 2 1 - e 2 = 4 a e ⇒ b 2 = 4 h ⇒ k 2 = 4 h ⇒ y 2 = 4 x ⇒ eccentricity = 1

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