Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Let the equation of the circle be

x² + y² + 2gx + 2fy + c = 0

Since it passes through the origin (0,0)

Substituting (0, 0) in this equation

c = 0

Substituting (0, a) in this equation

a² + 2af = 0

2af = -a²

f = = -

Substituting (b, 0) in this equation

b² + 2gb = 0

2gb = -b²

g = = -

Substituting the value of f and g in the general equation

x² + y² + n + = 0

Therefore the equation of the required circle is

x² + y² – bx – ay = 0