40 POINTS Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 4x + y2 − 6y = −4

Rewrite in standard form to find the center  

( h , k )  and radius  r .

Center:  ( − 2 , 3 )

Radius: 3

Step-by-step explanation:

 the center (h, k) is (-2, 3), and the radius r is 3

Step-by-step explanation:

Separate the x- and y-terms and complete the square for each. The square is completed by adding the square of half the linear term coefficient.

 (x^2 +4x +(4/2)^2) +(y^2 -6y +(-6/2)^2) = -4 +(4/2)^2 +(-6/2)^2

 (x +2)^2 +(y -3)^2 = 9

Compare to the form ...

 (x -h)^2 +(y -k)^2 = r^2

and you see that the center (h, k) is (-2, 3), and the radius r is 3.

2

step-by-step explanation:

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step-by-step explanation:

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