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Equation of chord $(\mathrm{AB})$ of circle $\mathrm{x^2+y^2=2}$ passing through the point $\mathrm{P(2,2)}$ , such that $\mathrm{\frac{P B}{P A}=3}$ , is

Option: 1
$\mathrm{x=3 y}$

Option: 2
$\mathrm{x=y}$

Option: 3
$\mathrm{y-2=\sqrt{3}(x-2)}$

Option: 4
none of these

Answers (1)

best_answer

As $\mathrm{\frac{P B}{P A}=3 \quad \Rightarrow \quad A B=(P B-P A)=2 \sqrt{2} \quad\left\{Q \quad(P A)(P B)=P T^2\right\}}$
As point $\mathrm{P}$ is $(2,2)$ and the given circle $\mathrm{x^2+y^2=2}$ has diameter $\mathrm{2 \sqrt{2}. }$

$\mathrm{\Rightarrow A B }$ is diameter of the circle.
$\mathrm{\Rightarrow }$ Line must pass through the centre $(0,0)$ also.

Hence option 2 is correct.

Posted by

Gautam harsolia

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