Question

Find the equations to the circles which pass through the points
$(0,0),(a,0)$, and $(0,b)$.

Answer 1

Suppose the equation of circle is $x^2+y^2-2hx-2ky+c=0$

(0,0) satisfies the equation, on putting it in the equation, we get $0+c=0$

$\Rightarrow c=0$

Intercepts on positive X and Y axis equal a and b respectively.

$\therefore$ Centre of the circle is at $(\frac{a}{2},\frac{b}{2})$

Thus, the equation of circle is $x^2+y^2-ax-by=0$