Question

The center of a circle is the point (3, 2). if the point (6, −2) lies on this circle, find the standard equation for the circle.

Answer 1

Given
centre of circle O(3,2)=O(x0,y0)
point on circle P(6,-2)

Standard equation of circle:
(x-x0)^2+(y-y0)^2=r^2

r=radius of circle
= (distance OP)
= sqrt((6-3)^2+(-2-2)^2)
=sqrt(3^2+(-4)^2)
=sqrt(25)

=>
r^2=(sqrt(25))^2=25

Equation of circle
(x-x0)^2+(y-y0)^2=r^2
(x-3)^2+(y-2)^2=25 ............... standard equation of circle