# How do you find the center and radius of the circle #x^2 + y^2 - 4x - 14y + 29 = 0#?

##### 1 Answer

The center will be at

#### Explanation:

This is an intriguing problem that requires several applications of math knowledge. The first of which is just determining what we need to know and what that might look like.

A circle has the generalized equation:

Where

Looking at the given equation, it seems like our best bet is going to be factoring the two polynomials presented (the one made up of the

Since those are the only square terms that would give us the appropriate first degree coefficient. But there's a problem!

But all we have is the

So putting it together we get:

which really is just:

Now that we have a standard form circle, we can see that the center will be at