JEE Advanced 2016 Paper 2 Mathematics Q17

Mathematics

Problem

PARAGRAPH 2 Let F1(x1,0)F_1(x_1,0) and F2(x2,0)F_2(x_2,0), for x1<0x_1<0 and x2>0x_2>0, be the foci of the ellipse x29+y28=1\frac{x^2}{9}+\frac{y^2}{8}=1. Suppose a parabola having vertex at the origin and focus at F2F_2 intersects the ellipse at point MM in the first quadrant and at point NN in the fourth quadrant. The orthocentre of the triangle F1MNF_1MN is

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