Question

can you help find the area of a circle centered at (1,1) that passes through the point (-2,6).

Answer 1

the circle's center is at (1,1) and passes through (-2,6)

meaning that the distance between (1,1) and (-2,6) is the "radius"
recall that the area of a circle = \(\bf \pi r^2\)

so find the distance for those 2 points to get the radius, then use the area of a circle's formula \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 1}}\quad ,&{\color{blue}{ 1}})\quad &({\color{red}{ -2}}\quad ,&{\color{blue}{ 6}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 2

find r by distance formula,then area
\[A=\pi r^2\]