Question

If a circle passes through (0, 0), (a, 0) and (0, b), then the coordinates of its centre are __________.

Answer 1

Given circle passes through (0, 0), (a, 0) and (0, b)


Since AB forms a diameter of circle
$$\begin{gathered} \mathrm{hence},\mathrm{center}\mathrm{of}\mathrm{the}\mathrm{circle}\mathrm{is}\left(\frac{a+0}{2},\frac{0+b}{2}\right) \\ \mathrm{i}.\mathrm{e}.\left(\frac{a}{2},\frac{b}{2}\right)\mathrm{is}\mathrm{the}\mathrm{center}\mathrm{of}\mathrm{the}\mathrm{circle} \end{gathered}$$