The orthocentre of the triangle F₁MN is- [JEE Adv 2016 P2]

Correct Answer is : (−910,0)≤ft(-9/10,0)(−109,0)

Correct Answer is : (−910,0)≤ft(-9/10,0)(−109,0)

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JEE Advanced 2016 Paper 2

Next 2 questions are based on the paragraph

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.

Section: Mathematics

Question : 53 of 54

Marks: +1, -0

F_1MN

Solution:

Equation of altitude through M :

y-\sqrt{6}=\frac{5}{2\sqrt{6}}=\frac{5}{2\sqrt{6}}\left(x-\frac{3}{2}\right)

Equation of altitude through

F_1: y=0

solving, we get orthocentre

-\frac{9}{10},0

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