2024/044) What is the equation of a circle which passes through three points $(0,0), (a,0),(0,b)$

 https://www.quora.com/What-is-the-equation-of-a-circle-which-passes-through-three-points-0-0-a-0-and-0-b

Because one point $(0,0)$  is origin, one point $(a,0)$ lies on x-axis and another $(0,b)$ on y axis it is clear that is is a right angled triangle. so the circumcenter is the midpoint of the hypotenuse that is $(\frac{a}{2},\frac{b}{2})$

so the equation of the circle is

$(x-\frac{a}{2})^2 +(y-\frac{b}{2})^2=(0-\frac{a}{2})^2 + (0-\frac{b}{2})^2$  the RHS is square of  distance of origin to to the centre

simplifying we get

$x^2-ax+y^2-by=0$