# How do you write the equation of the circle with d=12 and a center translated 18 units left and 7 units down from the origin?

Apr 21, 2016

${\left(x + 18\right)}^{2} + {\left(y + 7\right)}^{2} = 144$

#### Explanation:

Under a translation of $\left(\begin{matrix}- 18 \\ - 7\end{matrix}\right)$

the origin (0 , 0) → (0-18 , 0-7) → (-18 , -7)

The standard form of the equation of a circle is.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where (a , b) are the coordinates of the centre and r, the radius

here a = -18 , b = -7 and r = 12

$\Rightarrow {\left(x + 18\right)}^{2} + {\left(y + 7\right)}^{2} = 144 \text{ is the equation }$