Problem: Equation of chord AB of circle $x^2 + y^2 = 2$ passing through P(2 , 2) such that PB/PA = 3, is given by

(A) x = 3 y

(B) x = y

(C) y – 2 = √3(x – 2)

(D) none of these

Sol. Any line passing through (2, 2) will be of the form $\large \frac{y-2}{sin\theta} = \frac{x-2}{cos\theta} = r $

When this line cuts the circle x^{2} + y^{2} =2 ,

(rcosθ + 2)^{2} + (r sinθ + 2)^{2} = 2

⇒ r^{2} + 4(sinθ+ cosθ)r + 6 = 0

$\large \frac{PB}{PA} = \frac{r_2}{r_1} $ , now if r_{1} = α , r_{2} = 3α ,

then 4α = – 4(sinθ + cosθ), 3α^{2} = 6

⇒ sin2θ = 1

⇒ θ = π/4

So required chord will be y – 2 = 1 ( x –2)

y = x.