Let and , be the end points of the latusrectum of the ellipse . The equations of…

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let

P(x_1, y_1)

and

Q(x_2, y_2)

y_1 < 0, y_2 < 0

be the end points of the latusrectum of the ellipse

x^2 + 4y^2 = 4

. The equations of parabolas with latusrectum

PQ

are (1)

x^2 + 2\sqrt{3}y = 3 + \sqrt{3}

(2)

x^2 - 2\sqrt{3}y = 3 + \sqrt{3}

(3)

x^2 + 2\sqrt{3}y = 3 - \sqrt{3}

(4)

x^2 - 2\sqrt{3}y = 3 - \sqrt{3}