# How do you find the equation of a circle with center at the origin and passing through (-6,-2)?

##### 1 Answer

Mar 2, 2017

See below.

#### Explanation:

The equation of a circle with center

Because we know the circle is centered at the origin, i.e.

#r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

Given the points

#r=sqrt((-6-0)^2+(-2-0)^2)#

#=sqrt(36+4)#

#sqrt(40)=2sqrt(10)#

Therefore, the equation of the circle is given by:

#x^2+y^2=(2sqrt(10))^2#

graph{x^2+y^2=40 [-20, 20, -10, 10]}