# What is the standard form of the equation of a circle with center of a circle is at (-15,32) and passes through the point (-18,21)?

Nov 14, 2015

${\left(x + 15\right)}^{2} + {\left(y - 32\right)}^{2} = 130$

#### Explanation:

The standard form of a circle centred at (a,b) and having radius r is ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$.

So in this case we have the centre, but we need to find the radius and can do so by finding the distance from the centre to the point given :

d((-15,32);(-18,21))=sqrt((-18-(-15))^2+(21-32)^2)=sqrt130

Therefore the equation of the circle is

${\left(x + 15\right)}^{2} + {\left(y - 32\right)}^{2} = 130$