Question

Find the equation of the circle in center radius from given endpoints of a diameter (3,12) and (9,4)

Answer 1

ttp://www.mathwarehouse.com/geometry/circle/images/equation-of-circle/general-formula-equation-of-circle.png

Answer 2

http://www.mathwarehouse.com/geometry/circle/images/equation-of-circle/general-formula-equation-of-circle.png

those 2 points are the diameter.... so the center is half-way between them so \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&(3\quad ,&12)\quad &(9\quad ,&4)
\end{array}
\\\quad \\
\text{middle point of 2 points }\\
\left(\cfrac{x_2 + x_1}{2}\quad ,\quad \cfrac{y_2 + y_1}{2} \right)\Longleftarrow \color{red}{center, (h, k)}\\
\\ \quad \\
\text{distance between 2 points}\\
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\quad \Longleftarrow \color{red}{diameter}\\ \quad \\
radius = \cfrac{diameter}{2}
\)