Question

Which point lies on a circle that is centered at A(3, 3) and passes through B(6, 5)?
C(1, 6)
D(6, 0)
E(0, 3)
F(3, -1)
G(3, 6)

Answer 1

you could, use the circle formula to find the circle's equation
and then test the given coordinates, to see which one matches
or
use the distance formula to find the distance between A and B

and then test the given choices to see which one has the same distance with A

Answer 2

I'd think is simpler to just get the circle's equation first
and test about



to ge the radius then \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 3}})\quad
% (c,d)
&({\color{red}{ 6}}\quad ,&{\color{blue}{ 5}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}
\\ \quad \\
\textit{and use that radius, with the given center "A" for the formula}
\\ \quad \\

(x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2={\color{purple}{ r}}^2

\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
radius={\color{purple}{ r}}\)