How do you find the center and radius of the circle given 3x2+3y2+12x6y+9=0?

1 Answer
Nov 23, 2016

The center and radius are related to the coefficient of the equation.

Explanation:

First divide all the equation by three to put in simple form:

x2+y2+4x2y+3=0

Now consider the general equation of the circle is:

(xxo)2+(yyo)2R2=0

where the center is the point (xo,yo) and R is the radius.

Expanding:

x22xxo+x2o+y22yyo+y2oR2=0

Comparing similar terms, you can easily see that:

2xo=4xo=2
2yo=2yo=1
x2o+y2oR2=3R=2

graph{x^2+y^2+4x-2y+3=0 [-10.375, 9.625, -4.08, 5.92]}