Find $a$ in a graph

Question

Question

A circle of center $(-3 , -2)$ passes through the points $(0 , -6)$ and $(a , 0).$ Find $a$.

What I know

Well, you can say that these 2 points are equal distance to the centre, which means they are part of the circle.

Problem

But I do not know how to find $a$. Then I got no idea how to approach this question, so I do want some help please.

Answer 1

The distance between $(x,y)$ and $(u,v)$ is $\sqrt{(u-x)^2+(v-y)^2}$.

The distance between $(-3,-2)$ and $(0,-6)$ is $5$.

If $(a,0)$ is on the circle,

then the distance between $(-3,-2)$ and $(a,0)$ is also $5=\sqrt{(a+3)^2+2^2}$.

Can you solve for $a$?

Answer 2

Does this figure help? The radii are the same.