# How do you write the equation of a circle with the center (8,7) and radius r=6?

Mar 24, 2016

The equation is
${x}^{2} + {y}^{2} - 16 x - 14 y + 77 = 0$

#### Explanation:

As a circle is a point that moves so that its distance from a given point (called center) is always same (called radius), we should first calculate the distance of a point $\left(x , y\right)$ from the center at $\left(8 , 7\right)$ and that should be $6$, as radius is given to be $6$.

Hence $\sqrt{{\left(x - 8\right)}^{2} + {\left(y - 7\right)}^{2}} = 6$

Now squaring both sides, we get

${\left(x - 8\right)}^{2} + {\left(y - 7\right)}^{2} = 36$ or

${x}^{2} - 16 x + 64 + {y}^{2} - 14 y + 49 = 36$ or

${x}^{2} + {y}^{2} - 16 x - 14 y + 64 + 49 - 36 = 0$ or

${x}^{2} + {y}^{2} - 16 x - 14 y + 77 = 0$

graph{x^2+y^2-16x-14y+77=0 [-20, 20, -5, 15]}