Question

Write the equation of a circle with the following pints in the picture using the completing the square method. Thanks

Answer 1

So hmm notice the picture below

you have the center, and a point on the circle... all you need is the radius

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ -2}})\quad % (c,d) &({{ 3}}\quad ,&{{ -4}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\leftarrow r$

then use that radius in the circle's equation

$\bf (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad center\ ({{ h}},{{ k}})\qquad radius={{ r}}$