The equation of the circle with radius 5 whose centre lies on x -axis and passes through the point (

Question

The equation of the circle with radius 5 whose centre lies on x -axis and passes through the point ( 2,3 ) is

Professor PC Thomas Classes · Answer

Centre on x-axis is $(h,0)$. $(2-h)^2 + (3-0)^2 = 5^2 \implies (2-h)^2 + 9 = 25 \implies (2-h)^2 = 16 \implies 2-h = \pm 4 \implies h = -2$ or $6$. Using $h=-2$, eq is $(x+2)^2+y^2=25 \implies x^2+y^2+4x-21=0$.