What is the standard form of the equation of a circle with endpoints of a diameter at the points (7,8) and (-5,6)?

Mar 6, 2018

${\left(x - 1\right)}^{2} + {\left(y - 7\right)}^{2} = 37$

Explanation:

The center of the circle is the midpoint of the diameter, i.e. $\left(\frac{7 - 5}{2} , \frac{8 + 6}{2}\right) = \left(1 , 7\right)$

Again, the diameter is the distance between the points s$\left(7 , 8\right)$ and $\left(- 5 , 6\right)$ :

$\sqrt{{\left(7 - \left(- 5\right)\right)}^{2} + {\left(8 - 6\right)}^{2}} = \sqrt{{12}^{2} + {2}^{2}} = 2 \sqrt{37}$

so the radius is $\sqrt{37}$.

Thus the standard form of the circles equation is

${\left(x - 1\right)}^{2} + {\left(y - 7\right)}^{2} = 37$