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Ellipse question

2016 · Shift 2 · Q30

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2016 · Shift 2 · Q30

Ellipse question

2016 · Shift 2 · Q30

JEE AdvancedMathematicsEllipseMCQ+3 / −1

Let

{F_1}\left( {{x_1},0} \right)

and

{F_2}\left( {{x_2},0} \right)

for

{{x_1} \lt 0}

and

{{x_2} \gt 0}

, be the foci of the ellipse

{{{x^2}} \over 9} + {{{y^2}} \over 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

M{F_1}N{F_2}

is

A
$3:4$
B
$4:5$
C
$5:8$
D
$2:3$

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