# How do you find the equation of the circle given center at (5,2) and radius 6√6?

Jul 16, 2016

Equation of circle is
${x}^{2} + {y}^{2} - 10 x - 4 y - 187 = 0$

#### Explanation:

Let $\left(x , y\right)$ be a point on circle. As it's distance from center $\left(5 , 2\right)$ is equal to radius which is $6 \sqrt{6}$, hence

$\sqrt{{\left(x - 5\right)}^{2} + {\left(y - 2\right)}^{2}} = 6 \sqrt{6}$ or

(x-5)^2+(y-2)^2)=(6sqrt6)^2 or

x^2-10x+25+y^2-4y+4=36×6 or

${x}^{2} + {y}^{2} - 10 x - 4 y + 25 + 4 - 216 = 0$ or

${x}^{2} + {y}^{2} - 10 x - 4 y - 187 = 0$