SOLUTION: x^2+4x+y^2+6y=2 What is the center and the radius?

Question 192331: x^2+4x+y^2+6y=2
What is the center and the radius?
Found 2 solutions by Alan3354, RAY100:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
x^2+4x+y^2+6y=2
What is the center and the radius?
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Complete the squares for x and y:
x^2+4x+4 + y^2+6y+9 = 2+4+9
(x+2)^2 + (y+3)^3 = 15
The center is (-2,-3)
The radius is sqrt(15)

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
basic formula for a circle is
(x-h)^2 + (y-k)^2 = r^2, where h is x center, k is y center, r is radius
to fit this form the given problem must "complete the square"
(x^2 +4x +4) + (y^2 +6y+9) = 2 + (+4)+ (+9)
reviewing take coefficient of the middle term, 4x, divide by 2 and then square, (4/2)^2 =4 and add to both sides of eqn
for y terms, ( 6/2)^2 =9 and add to both sides
Now factor x and y sets
(x+2)^2 + (y+3)^2 = 15
comparing to basic form we find
x center is (-2)
y center is (-3)
rad^2 = 15, rad =sq rt 15 = 3.87
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