Question

find the center and the radius of the following circle
x² - 16x + y² + 12y = 0
the center is
(type an ordered pair.)
the radius is
(simplify your answer.)
use the graphing tool to graph the circle.
click to enlarge graph

Explanation:

Step1: Complete the square for x - terms

We have $x^{2}-16x$. To complete the square, we take half of the coefficient of x (-16), square it. Half of - 16 is -8, and $(-8)^{2}=64$. So we add 64 to both sides of the equation: $x^{2}-16x + 64+y^{2}+12y=64$.

Step2: Complete the square for y - terms

We have $y^{2}+12y$. Half of 12 is 6, and $6^{2}=36$. We add 36 to both sides of the equation: $x^{2}-16x + 64+y^{2}+12y+36=64 + 36$.

Step3: Rewrite in standard form

The left - hand side can be written as $(x - 8)^{2}+(y + 6)^{2}$, and the right - hand side is 100. So the equation of the circle in standard form is $(x - 8)^{2}+(y+6)^{2}=100$.
The standard form of a circle is $(x - a)^{2}+(y - b)^{2}=r^{2}$, where (a,b) is the center and r is the radius.

Answer:

The center is $(8,-6)$.
The radius is $10$.