Here , we are given with a circle on cartesian plane , and we need to find the equation of the circle , We are also given that it's centre is at (5,-6) { From graph } and it's radius is 3 units . Now , as we know, the standard equation of a circle is [tex]{\bf (x-h)^{2}+(y-k)^{2}=r^{2}}[/tex] where (h,k) is the centre of the circle and radius is r . Now , our equation will be ;
[tex]{:\implies \quad \sf (x-5)^{2}+\{y-(-6)\}^{2}=3^{2}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{(x-5)^{2}+(y+6)^{2}=9}}}[/tex]
This is the required equation of Circle
Or if you want to proceed it further , then you will get x² + y² - 10x + 12y + 50 = 0