Question

Write the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8).

Answer 1

Notice the picture below

$\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad center\ ({{ h}},{{ k}})\qquad radius={{ r}}\\\\ -----------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 4}})\quad % (c,d) &({{ 4}}\quad ,&{{ 8}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\leftarrow r$

you have the center, the h,k, all  you really need is the radius "r"