Question

"Complete the square" to convert the equation of each circle to graphing form. Identify the center and the radius.

x² + 6x + y2 – 4y= -9
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Answer 1

The center is (-3,2) and the radius is r=2

Explanation:

The general equation of the given circle is

`x^2+6x+y^2-4y=-9`

Add the square of half the coefficient of the linear terms to both sides of the equation to obtain;

`x^2+6x+3^2+y^2-4y+(-2)^2=-9+3^2+(-2)^2`

`x^2+6x+9+y^2-4y+4=-9+9+4`

`x^2+6x+9+y^2-4y+4=4`

The quadratic trinomials in x and y on the left side of the equations are perfect squares.

We factor to obtain;

`(x+3)^2+(y-2)^2=4`

`(x--3)^2+(y-2)^2=2^2`

Comparing to:

`(x-h)^2+(y-k)^2=r^2`

The center is (-3,2) and the radius is r=2