Let x^2=4ky,k0 be a parabola with vertex A. Let BC be its latusrectum. An ellipse with centre on BC touches the parabola at A, and cuts BC at points…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (C) √53. Given, x^2=4ky BC is latusrectum. ∴BC=4k BD=DE=EC ∴DE=BC/3=4k/3 P is centre of ellipse. ∴PE=2k/3 OP=k ∵ Eccentricity of ellipse √(1-PE^2OP^2)=√(1-4k^29k^2) ⇒e=√(9-49)=√53

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

Solution

More Ellipse Questions

Let x2=4ky,k>0 be a parabola with vertex A. Let BC be its latusrectum. An ellipse with centre on BC touches the parabola at A, and cuts BC at points D and E such that BD=DE=EC (B, D, E, C in that order). The eccentricity of the ellipse is

Solution

More Ellipse Questions

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