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Parabola question

2022 · 29 Jul · Shift 1 · Q37
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  5. /2022 · 29 Jul · Shift 1 · Q37

Parabola question

2022 · 29 Jul · Shift 1 · Q37

JEE MainMathematicsParabolaMCQ+4 / −1
Let the focal chord of the parabola P:y2=4x\mathrm{P}: y^{2}=4 xP:y2=4x along the line L:y=mx+c,m>0\mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \mathrm{m}\gt 0L:y=mx+c,m>0 meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola H:x2−y2=4\mathrm{H}: x^{2}-y^{2}=4H:x2−y2=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 :
  1. A
    262 \sqrt{6}26​
  2. B
    2142 \sqrt{14}214​
  3. C
    464 \sqrt{6}46​
  4. D
    4144 \sqrt{14}414​
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