find the equation of the circle passing through origin and cutting off intercepts a and b from x axis and y axis

Since, the circle cuts intercepts of a and b on the x – axis and y – axis respectively, therefore, the line joining the points (a, 0) and (0, b) will be the diameter of the circle.

Let the co-ordinates of the centre of the circle be h and k respectively.

Therefore, h = (a + 0)/2 and k = (b + 0)/2 

Let the radius of the circle be r

Therefore, r² = (0.5a – a)²

 + (0.5b – 0)²

Equation of the circle is as follows:

(x – h)² + (y – k)² = r²

Equation: x² + y² – ax – by = 0