# How do you write an equation for the translation of x^2 + y^2 = 25 by 7 units left and 2 units down?

Oct 17, 2016

The equation of the translated circle is:
${\left(x + 7\right)}^{2} + {\left(y + 2\right)}^{2} = 25$.

#### Explanation:

The standard form of a circle is
${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$,
where $r$ is the radius of the circle and $\left(h , k\right)$ is the center of the circle.

In ${x}^{2} + {y}^{2} = 25$, the center is at $\left(0 , 0\right)$. When the circle is translated left 7 units, it means that the new center has $h = - 7$. Translating the circle down 2 units means that the new center has $k = - 2$. So, the translated circle has the equation

${\left(x + 7\right)}^{2} + {\left(y + 2\right)}^{2} = 25$.