JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let a line \(\mathrm{y}=\mathrm{mx}(\mathrm{m}>0)\) intersect the parabola, \(\mathrm{y}^{2}=\mathrm{x}\) at a point \(\mathrm{P},\) other than the origin. Let the tangent to it at \(P\) meet the \(x\) -axis at the point \(Q\). If area \((\Delta \mathrm{OPQ})=4\) sq. units, then \(\mathrm{m}\) is equal to
- A \(1.5\)
- B \(0.5\)
- C \(1.33\)
- D \(1.67\)
Answer & Solution
Correct Answer
(B) \(0.5\)
Step-by-step Solution
Detailed explanation
\(\Delta \mathrm{OPQ}=4\) \(\frac{1}{2}\left|\begin{array}{ccc}{0} & {0} & {1} \\ {t^{2}} & {t} & {1} \\ {-t^{2}} & {0} & {1}\end{array}\right|=4\) \(\mathrm{t}=2(\because \mathrm{t}>0)\) \(\therefore m=\frac{1}{2}\) Ans. \(0.50\)
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