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Tangents are drawn to the circle \mathrm{x^{2}+y^{2}=50} from a point \mathrm{'p'} lhying on the \mathrm{x}-axis. These tangents meet the  -axis at points '\mathrm{P} 1'and '\mathrm{P} 2'. Possible coordinates of '\mathrm{P} 'so that area of triangle P1P2 is minimum, is/are 

Option: 1

(10,0)


Option: 2

(10 \sqrt{2}, 0)


Option: 3

(-11,0)


Option: 4

(-10 \sqrt{2}, 0)


Answers (1)

best_answer

\begin{aligned} & O P=5 \sqrt{2} \sec \theta \\ & O P_{1}=5 \sqrt{2} \operatorname{cosec} \theta \end{aligned}

\triangle P P_{1} P_{2}=\frac{100}{\sin 2 \theta}
\left(\triangle P P_{1}, P_{2}\right)_{\min }=100

\Rightarrow \theta=\frac{\pi}{4} \Rightarrow O P=10
\Rightarrow \quad \mathrm{P}=(10,0),(-10,0)
Hence (a) is correct

Posted by

HARSH KANKARIA

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