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JEE Main 202125 JulyMorning Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Morning Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2021 · 25 July · Morning Shift · Mathematics · Parabola

Let a parabola P be such that its vertex and focus lie on the...

Let a parabola PP be such that its vertex and focus lie on the positive xx-axis at a distance 22 and 44 units from the origin, respectively. If tangents are drawn from O(0,0)O ( 0, 0 ) to the parabola PP which meet PP at SS and RR, then the area (in sq. units)ofδSORof \delta SOR is equal to :Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance 2 and 4 units from the

Options

  1. A16216\sqrt{2}
  2. B1616
  3. C3232
  4. D828\sqrt{2}

Correct answer

B. 1616

Step-by-step solution

Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance 2 and 4 units from the

From the diagram, clearly RSRS is latus-rectum

∵VF=(4−2)2+(0−0)2=2=a∵ VF = \sqrt{{\left(4 - 2\right)}^{2} + {\left(0 - 0\right)}^{2}} = 2 = a

∴RS=4a=8∴ RS = 4a = 8

Now OF=2a=4OF = 2a = 4

So, the area of triangle ORS=12×4×8=16ORS = \dfrac{1}{2} \times 4 \times 8 = 16

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