Question

Find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.)

Answer 1

$(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \\---------------------------\\ \qquad center\ ({{ h}},{{ k}})\qquad radius={{ r}} \\ \quad \\ \textit{we know the center}\implies center\ ({{ 6}},{{ 8}}) \\ \quad \\ \textit{what's the radius "r"?} \\ \quad \\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) Center&({{ 6}}\quad ,&{{ 8}})\quad % (c,d) P&({{ 4}}\quad ,&{{ 1}}) \end{array}\qquad % distance value r= \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

find "r", then plug it in the circle's equation