Q. The line $x = y$ touches a circle at the point $(1, 1)$. If the circle also passes through the point $(1, -3)$, then its radius is :
Solution:
Equation of circle can be written as $(x -1)^2 + (y -1)^2 + l(x -y) = 0$
It passes through (1, -3)
$16 + \lambda (4) = 0 \; \Rightarrow \; \lambda = -4$
So $(x -1)^2 + (y -1)^2 -4(x -y) = 0$
$ \Rightarrow \; x^2 + y^2 - 6x + 2y + 2 = 0$
$\Rightarrow \; r = 2 \sqrt{2}$
