Question

If (m, 2) is on a circle with center (−3, 2) and radius 8, what is a value of m?

Answer 1

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 2}})\quad % (c,d) &({{ m}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

$\bf \textit{we know the distance from m,2 and -3,2(center) is the radius} \\\\\\ d=8\implies 8=\sqrt{[m-(-3)]^2+[2-2]^2} \\\\\\ 8=\sqrt{(m+3)^2+(0)^2}\implies 8=\sqrt{(m+3)^2}\implies 8^2=(m+3)^2 \\\\\\ 64=(m+3)^2\implies \sqrt{64}=\sqrt{(m+3)^2}\implies 8=m+3 \\\\\\ 8-3=m$