What is the standard form of the equation of a circle with center (-3,6) and the radius is 4?

May 16, 2016

${\left(x + 3\right)}^{2} + {\left(y - 6\right)}^{2} = 16$

Explanation:

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 coords of centre and r, the radius.

Here the centre = (-3 ,6) → a =-3 and b = 6 , r = 4

Substituting these values into the standard equation

$\Rightarrow {\left(x + 3\right)}^{2} + {\left(y - 6\right)}^{2} = 16$