Question 993571
(6,0) and (24,0) both lie on x-axis, hence mid point of these points will lie directly below( or above) centre (Since line joining centre to mid point of a chord is perpendicular to the chord)
Also, since the circle touches the y axis, so distance from origin to this mid point found above will be equal to radius.
Now mid point is ((6+24)/2,(0+0)/2) i.e. (15,0)
So radius is 15.
Now let distance of centre from mid point found above be p
So, {{{r^2 = p^2 + ((24-6)/2)^2}}}   (DRAW DIAGRAM TO UNDERSTAND ALL THE STEPS)
i.e. {{{15^2 = p^2 + 9^2}}}
=>  p = 12 or p = -12
So coordinates of centre will become (15,12) or (15,-12)
So, the equation of circle,
{{{(x-15)^2 + (y-12)^2 = 15^2}}} or {{{(x-15)^2 + (y+12)^2 = 15^2}}}
=> {{{x^2 + y^2 - 30x - 24y +144 = 0}}} or {{{x^2 + y^2 - 30x + 24y +144 = 0}}}

(DRAW DIAGRAM TO UNDERSTAND ALL THE STEPS)