Let $F _ { 1 } \left( x _ { 1 } , 0 \right)$ and $F _ { 2 } \left( x _ { 2 } , 0 \right)$, 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 $M Q R$ to area of the quadrilateral $M F _ { 1 } N F _ { 2 }$ is (A) $3 : 4$ (B) $4 : 5$ (C) $5 : 8$ (D) $2 : 3$
Let $F _ { 1 } \left( x _ { 1 } , 0 \right)$ and $F _ { 2 } \left( x _ { 2 } , 0 \right)$, 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 $M Q R$ to area of the quadrilateral $M F _ { 1 } N F _ { 2 }$ is\\
(A) $3 : 4$\\
(B) $4 : 5$\\
(C) $5 : 8$\\
(D) $2 : 3$