# If a circle passes through the point (0, 0) (a, 0), (0, b) then find the coordinates of its centre.

Toolbox:
• The general equation of the circle is given by $x^2 + y^2 + 2gx + 2fy + c = 0$, where the centre is $(-g, -f)$
Given the point $(0,0)$, Equation of the circle through that point is $c = 0$
Given the point $(a,0)$, Equation of the circle through that point is $a^2+2ga+c = 0$
$\Rightarrow a^2+2ag = 0 \rightarrow a (a+2g) = 0 \rightarrow g = -\large\frac{a}{2}$
Given the point $(0,b)$, Equation of the circle through that point is $b^2+2fb+c = 0$
$\Rightarrow b^2+2fb = 0 \rightarrow b (b+2f) = 0 \rightarrow f = -\large\frac{b}{2}$
We know that the centre of the circle = $(-g, -f) = (\large\frac{a}{2}$$.\large\frac{b}{2}$$)$