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Tangents are drawn to the circle  \mathrm{x^2+y^2=50} from a point 'P' lying on the X-axis. These tangents meet

the Y-axis at points  \mathrm{\mathrm{P}_1} and \mathrm{\mathrm{P}_2} . Possible coordinates of 'P' so that area of triangle \mathrm{\mathrm{PP}_1 \mathrm{P}_2}  is minimum,

is/are

Option: 1

(10,2)


Option: 2

\mathrm{(10 \sqrt{2}, 0)}


Option: 3

(-10,0)


Option: 4

\mathrm{(-10 \sqrt{2}, 0)}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mathrm{OP}=5 \sqrt{2} \sec \theta \\\\ & \mathrm{OP}_1=5 \sqrt{2} \operatorname{cosec} \theta \\\\ & \text { area }\left(\Delta \mathrm{PP}_1 \mathrm{P}_2\right)=\frac{100}{\sin 2 \theta}, \text { area }\left(\Delta \mathrm{PP}_1 \mathrm{P}_2\right)_{\min }=100 \\\\ & \Rightarrow \quad \theta=\pi / 4 \Rightarrow \mathrm{OP}=10 \\\\ & \Rightarrow \quad \mathrm{P}=(10,0),(-10,0) \end{aligned}}

 

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Pankaj

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