Question

Equation of chord AB of circle $x^2+y^2=2$ passing through P(2, 2) such that $\frac{PB}{PA}=3$, is given by

• A. $x=3y$
• B. $x=y$
• C. $y-2=\sqrt{3}(x-2)$
• D. $noneofthese$

Answer 1

The correct option is B

$x=y$

Let P = (2, 2)
$\frac{PB}{PA}=3\Rightarrow PB=3.PA$
We have $PA.PB=S_{11}$
$\Rightarrow 3P{A}^2=6$
$\Rightarrow PA=\sqrt{2}\Rightarrow PB=3\sqrt{2}$
$\therefore A=(2-\sqrt{2}cos\theta ,2-\sqrt{2}sin\theta )$ lies on circle
$\therefore (2-\sqrt{2}cos\theta {)}^2+(2-\sqrt{2}sin\theta {)}^2=2$
$\Rightarrow cos\theta +sin\theta =\sqrt{2}$
$\Rightarrow \theta =\frac{\pi }{4}$
$\therefore$ slope of AB = 1
$\therefore$ Equation of AB is x = y