Let x 2 = 4 k y , k 0 be a parabola with vertex A . Let B C be its latusrectum. An ellipse with centre on B C touches the parabola at A , and cuts B C at points D and E such that B D = D E = E C ( B , D , E , C in that order). The eccentricity of the ellipse is

Question

Let x 2 = 4 k y , k > 0 be a parabola with vertex A . Let B C be its latusrectum. An ellipse with centre on B C touches the parabola at A , and cuts B C at points D and E such that B D = D E = E C ( B , D , E , C in that order). The eccentricity of the ellipse is, 1 2, 1 3, 5 3, 3 2

MARKS App · Accepted Answer

Given, x 2 = 4 k y B C is latusrectum. ∴ B C = 4 k B D = D E = E C ∴ D E = B C 3 = 4 k 3 P is centre of ellipse. ∴ P E = 2 k 3 O P = k ∵ Eccentricity of ellipse 1 - P E 2 O P 2 = 1 - 4 k 2 9 k 2 ⇒ e = 9 - 4 9 = 5 3

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