JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
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 \(\mathrm{P}\) at \(\mathrm{S}\) and \(\mathrm{R}\), then the area (in \(sq.\, units\)) of \(\triangle \mathrm{SOR}\) is equal to:
- A \(16 \sqrt{2}\)
- B \(32\)
- C \(16\)
- D \(8 \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
Clearly \(Rs\) is latus-rectum \(\because \mathrm{VF}=2=\mathrm{a}\) \(\therefore \mathrm{RS}=4 \mathrm{a}=8\) Now OF \(=2 \mathrm{a}=4\) \(\Rightarrow\) Area of traingle \(ORS\) \(=16\)
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