# How do you find the equation of the circle given Center (8,-8), Radius 1/3?

Sep 17, 2016

$9 {x}^{2} + 9 {y}^{2} - 144 x + 144 y + 1151 = 0$

#### Explanation:

Circle with the given center at $\left(8 , - 8\right)$ and radius $\frac{1}{3}$,

is the locus of a point that moves so that it is always at a distance of $\frac{1}{3}$ from point $\left(8 , - 8\right)$

Hence equation is ${\left(x - 8\right)}^{2} + {\left(y - \left(- 8\right)\right)}^{2} = {\left(\frac{1}{3}\right)}^{2}$

or ${x}^{2} - 16 x + 64 + {y}^{2} + 16 y + 64 = \frac{1}{9}$

or $9 {x}^{2} + 9 {y}^{2} - 144 x + 144 y + 9 \times \left(64 + 64\right) - 1 = 0$

or $9 {x}^{2} + 9 {y}^{2} - 144 x + 144 y + 1151 = 0$

graph{9x^2+9y^2-144x+144y+1151=0 [4.894, 9.894, -8.68, -6.18]}