# How do you find the center and radius for x^2 + y^2 +2x -2y -14 = 0?

Aug 6, 2016

The circle has the center in (-1;1) and the radius of $4$

#### Explanation:

To find the center and radius we have to transform the equation to form:

## ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

We start from:

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

We transform it to:

${x}^{2} + 2 x \textcolor{red}{+ 1} + {y}^{2} - 2 y \textcolor{red}{+ 1} - 14 \textcolor{red}{- 2} = 0$

I added $1$ to transform the formulas to ${\left(a \pm b\right)}^{2}$. If I added $2$ then I had to substract $2$ to keep the equation balanced. These operation are marked in red.

${\left(x + 1\right)}^{2} + {\left(y - 1\right)}^{2} - 16 = 0$

${\left(x + 1\right)}^{2} + {\left(y - 1\right)}^{2} = 16$

From this equation we read that: the centre is (-1;1) and the radius is $r = 4$