# How do you write the equation of the locus of all points in the coordinate plane 10 units from (–6, 9)?

Oct 6, 2016

circle with equation ${\left(x + 6\right)}^{2} + {\left(y - 9\right)}^{2} = 100$

#### Explanation:

The points will lie on the circumference of a circle with centre (-6 ,9) and radius of 10.
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 = -6 , b = 9 and r = 10

${\left(x - \left(- 6\right)\right)}^{2} + {\left(y - 9\right)}^{2} = {10}^{2}$

$\Rightarrow {\left(x + 6\right)}^{2} + {\left(y - 9\right)}^{2} = 100 \text{ is the equation of the locus}$