# How do you find the center and radius of the circle given #x^2-12x+84=-y^2+16y#?

##### 2 Answers

Center (6, 8) and radius = 4

#### Explanation:

rewrite equation as

x^2 - 12x +y^2-16y +84 =0

(x^2 -12x +36) + (y^2-16y +64) +84 -36-64 =0

(x-6)^2 +(y-8)^2 -16 =0

(x-6)^2 +(y-8)^2 = 16 = 4^2

So center is (6,8) and radius 4

Write the equation as:

Center:

Radius: 4

#### Explanation:

You need to put the equation into standard form:

because we know that

In the given equation, move the constant term to the right and all of the other terms to the left:

Add

Because

Substitute 36 for every

We know that the left side is a perfect square and the right side simplifies a bit:

We do the same thing for the middle term to find

Substitute 64 for every

We know that the left is a perfect square and the right side simplifies:

Make the radius obvious by writing the ride side as a square: