Standard Circles
Standard Circles
How do you write the equation of a circle in standard form?
How do you write the equation of a circle in standard form and find the center and radius given the equation:
2x^2 + 2y^2 + 4x – 12y +11 = 0
I tried the completing the square method, but I forgot what to do when the the squared term has a coefficient that isn’t 1.
Thank You for any help you can offer.
2x^2 + 2y^2 + 4x – 12y +11 = 0
divide by 2
x^2 + y^2 + 2x – 6y +11/2 = 0
x^2 + 2x + y^2 – 6y +11/2 = 0
x^2 + 2x +1 + y^2 – 6y +11/2 = 0 + 1
(x+1)^2 + y^2 – 6y + 9 +11/2 = 0 + 1 + 9
(x+1)^2 + (y-3)^2 + 11/2 = 0 + 1 + 9
(x+1)^2 + (y-3)^2 = 0 + 1 + 9 – 11/2
(x+1)^2 + (y-3)^2 = 9/2
Hope this helps!
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