Let the focal chord of the parabola … along the line … meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola …. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is :

Parabola

JEE Main 2022 · 29 Jul, Morning shift · Q4673

MathematicsHard92×since 2002Q4673

Let the focal chord of the parabola

\mathrm{P}: y^{2}=4 x

along the line

\mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \mathrm{m}>0

meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola

\mathrm{H}: x^{2}-y^{2}=4

. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is :