Question

Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).

Answer 1

The equation of the required circle is ${\left(x-1\right)}^2+{\left(y-2\right)}^2=a^2$.
The circle passes through (−2, 6).
∴ ${\left(-2-1\right)}^2+{\left(6-2\right)}^2=a^2$
$$\begin{gathered} \Rightarrow 9+16=a^2 \\ \Rightarrow a=5 \end{gathered}$$

∴ Area of the required circle = ${\mathrm{\pi a}}^2=\mathrm{\pi }{\left(5\right)}^2=25\mathrm{\pi }\mathrm{square}\mathrm{units}$