# How do you find the general form of the equation of this circle given center (10, -1), radius = 10?

Mar 6, 2018

${x}^{2} + {y}^{2} - 20 x + 2 y + 1 = 0$

#### Explanation:

The equation of the circle with center (h,k) and radius r is:
$\textcolor{red}{{\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}}$
We have, $h = 10 , k = - 1. r = 10$
So,
${\left(x - 10\right)}^{2} + {\left(y + 1\right)}^{2} = {10}^{2}$$\Rightarrow {x}^{2} - 20 x + 100 + {y}^{2} + 2 y + 1 = 100$
$\Rightarrow {x}^{2} + {y}^{2} - 20 x + 2 y + 1 = 0$