jee-advanced 2016 Q53

jee-advanced · India · paper2 Conic sections Triangle or Quadrilateral Area and Perimeter with Foci

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.
The orthocentre of the triangle $F _ { 1 } M N$ is
(A) $\left( - \frac { 9 } { 10 } , 0 \right)$
(B) $\left( \frac { 2 } { 3 } , 0 \right)$
(C) $\left( \frac { 9 } { 10 } , 0 \right)$
(D) $\left( \frac { 2 } { 3 } , \sqrt { 6 } \right)$

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.

The orthocentre of the triangle $F _ { 1 } M N$ is\\
(A) $\left( - \frac { 9 } { 10 } , 0 \right)$\\
(B) $\left( \frac { 2 } { 3 } , 0 \right)$\\
(C) $\left( \frac { 9 } { 10 } , 0 \right)$\\
(D) $\left( \frac { 2 } { 3 } , \sqrt { 6 } \right)$

Paper Questions

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