# The ends of diameter (6,5) and (-12,-5), how do you find the equation of this circle?

Jan 11, 2016

${\left(x + 3\right)}^{2} + {y}^{2} = 106$

#### Explanation:

The centre of the circle is the midpoint of the points.
i.e. (-3,0)

The radius of the circle is half the distance between the points.

Distance = $\sqrt{{\left(6 - - 12\right)}^{2} + {\left(5 - - 5\right)}^{2}}$
$= \sqrt{{18}^{2} + {10}^{2}} = \sqrt{324 + 100} = \sqrt{424} = 2 \sqrt{106}$

Radius = $\sqrt{106}$

Equation: ${\left(x + 3\right)}^{2} + {y}^{2} = 106$