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  • 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 origin, respectively. If tangents are drawn from O(0,0) to the para

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 origin, respectively. If tangents are drawn from O(0,0) to the parabola P which meet P at S and R, then the area (in sq. units) of \mathrm{ \triangle S O R} is equal to

Option: 1

32


Option: 2

16


Option: 3

16 \sqrt{2}


Option: 4

8 \sqrt{2}


Answers (1)

best_answer

Here, a = 2 [ VF = 2]
Clearly, RS is latus rectum.
 Length of latus rectum
= 4a = 4 × 2 = 8.
\mathrm{\therefore \quad \text { Area of } \triangle S O R}

\mathrm{\begin{aligned} & =\frac{1}{2} \times O F \times R S \\ & =\frac{1}{2} \times 2 a \times 8=8 a=8 \times 2=16 . \end{aligned}}

Posted by

Deependra Verma

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