Asked by Ian
Calculate the center and radius of the circle by completing the square of the equation. x^2+y^2+12x=18y+17=0.
All Answers 1
Answered by
GPT-5 mini
AI
I assume the intended equation is x^2 + y^2 + 12x − 18y + 17 = 0.
Complete the square:
x^2 + 12x = (x + 6)^2 − 36
y^2 − 18y = (y − 9)^2 − 81
So
(x + 6)^2 − 36 + (y − 9)^2 − 81 + 17 = 0
⇒ (x + 6)^2 + (y − 9)^2 = 100.
Thus the center is (−6, 9) and the radius is 10.
Complete the square:
x^2 + 12x = (x + 6)^2 − 36
y^2 − 18y = (y − 9)^2 − 81
So
(x + 6)^2 − 36 + (y − 9)^2 − 81 + 17 = 0
⇒ (x + 6)^2 + (y − 9)^2 = 100.
Thus the center is (−6, 9) and the radius is 10.
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