Let and for , be the foci of the ellipse . Suppose a parabola having vertex at the…

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

Problem

Let

F_1(x_1, 0)

and

F_2(x_2, 0)

for

x_1 < 0

and

x_2 > 0

, be the foci of the ellipse

\frac{x^2}{9} + \frac{y^2}{8} = 1

. Suppose a parabola having vertex at the origin and focus at

F_2

intersects the ellipse at point

M

in the first quadrant and at point

N

in the fourth quadrant. If the tangents to the ellipse at

M

and

N

meet at

R

and the normal to the parabola at

M

meets the

X

-axis at

Q

, then the ratio of area of the triangle

MQR

to area of the quadrilateral

MF_1NF_2

is (1) 3 : 4 (2) 4 : 5 (3) 5 : 8 (4) 2 : 3