Question

please answer this question as fast as possible, with step by step explanations.

I will surely mark the appropriate answer as brainliest ​

Answer 1

Answer:

First find centre and radius of circle which is

( 1, 1 ) and 1 .

Let a point P ( x , y ) on line .

Now see picture Circumcircle of ∆PAB will go through all three points . angle OAP is right angle ( Tangent and radius ) . Which is only possible if OP is diameter of circumcircle so circumcetre will be mid point of OP .

Let circum-centre centre (h , k)

$h = \frac{1 + x}{2} \: \: \: \: and \: \: \: \: k = \frac{1 + y}{2} \\ \\ x = 2h - 1 \: \: \: \: and \: \: \: \: y = 2k - 1$

But ( x , y ) lies on line lx+my+n=0

$l(2h - 1) + m(2k - 1) + n = 0 \\ 2lh + 2mk + n - l - m = 0 \\ \\replace\:\: (h \: \: , \: k) \: \: \: by \: \: \:\:\: (x \: \: ,\: y) \\ \\ 2lx + 2my+ n - l - m = 0$