Question

find the equation of circle which passes through the point on the x axis which are at distances from the origin and the radius is 5​

Answer 1

if distance from origin is 3

Given r = 5, passes through points on x-axis at a distance 3 from the origin ⇒ The points are (3,0) and (-3,0) Let x2 + y2 + 2gx + 2fy + c = 0 is required equation (3,0)6g + C + 9 = 0 … (1) (-3,0) -6g + C + 9 = 0 …. (2) r = 5; 25 = g2 + f2 -C Adding 1 and 2 we get c = -9 and g = 0 and f = ±4 ∴ The required equation is x2 + y2 + 8y – 9 = 0