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