JEE Advanced 2016 Paper 2 Mathematics Q18

Mathematics

Problem

PARAGRAPH 2 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