Question

The area of the circle passing through the point (4, 6) and having centre at (1, 2) is __________.

Answer 1

Since center of circle is (1, 2) equation of circle is

$$\begin{gathered} {\left(x-1\right)}^2+{\left(y-2\right)}^2=r^2 \\ \mathrm{also}\mathrm{given}\mathrm{the}\mathrm{circle}\mathrm{passes}\mathrm{through}\left(4,6\right) \\ \therefore {\left(4-1\right)}^2+{\left(6-2\right)}^2=r^2 \\ 9+16=r^2 \\ \mathrm{i}.\mathrm{e}.r^2=25 \\ \therefore \mathrm{Area}\mathrm{of}\mathrm{circle}\mathrm{is}{\mathrm{\pi r}}^2 \\ =\mathrm{\pi }\left(25\right) \\ =25\mathrm{\pi }\mathrm{square}\mathrm{units} \\ \mathrm{i}.\mathrm{e}.25\mathrm{\pi }\mathrm{sqaure}\mathrm{units} \end{gathered}$$