Question

Find the equation of the circle with center ( − 5 , − 9 ) (-5,-9) and passes through the point ( − 2 , − 13 )

Answer 1

Given 
centre of circle O(-5,-9)=O(x0,y0)
point on circle P(-2,-13)

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

r=radius of circle
= (distance OP)
= sqrt((-2-(-5))^2+(-13-(-9))^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+5)^2+(y+9)^2=25   ............... standard equation of circle