Question

Find the equation of the circles passing through the point $(-4,3)$ and center at point of intersection of the lines $x+y=2,x-y=2$.

Answer 1

but $x^2+y^2+2px+2fy+c=0$ be circle

putting through (-6,3)

$16+9-8g+6f+c=0$

$\Rightarrow 8g-6f-c=25...\left(1\right)$

P I of $x+y=2$

$x-y=2$

$\Rightarrow x=2,y=0$

$(-g,-f)=(2,0)g=-2f=0$

put in (1)

$-16-c=25$

$c=-41$

$\therefore$ equation $x^2+y^2-6x-41=0$