Question

Find coordinate of the centre of a circle passing through the points $(6,-6),(3,-7)$ and $(3,3)$.

Answer 1

R.E.F image

As let the center of the circle be (h,k)

$\therefore \sqrt{(h-6{)}^2+(k+6{)}^2}=\sqrt{(h-3{)}^2+(k+7{)}^2}=\sqrt{(h-3{)}^2+(k-3{)}^2}$

$\therefore (h-6{)}^2+(k+6{)}^2=(h-3{)}^2+(k+7{)}^2=(h-3{)}^2+(k-3{)}^2$

Taking $(h-3{)}^2+(k+7{)}^2=(h-3{)}^2+(k-3{)}^2$

$\therefore k+7=-k+3$

$\Rightarrow 2k=-4$

$\Rightarrow k=-2$

$(h-6{)}^2+(k+6{)}^2=(h-3{)}^2+(k+7{)}^2$

$\Rightarrow (h-6{)}^2+(6-2{)}^2=(h-3{)}^2+(5{)}^2$

$\Rightarrow h^2+36-12h+16=h^2+9-6h+25$

$\Rightarrow 52-34=6h$

$\Rightarrow 6h=18$

$\Rightarrow h=3$

$\therefore$ center (3,-2)