Calculate the center and radius of the circle by completing the square of the equation x2+y2+12x−18y+17=0 .

Answer 1

To find the center and radius of the circle, we need to rewrite the equation in standard form by completing the square for both x and y terms.

Starting with the x terms:
x^2 + 12x = x^2 + 12x + 36 - 36 = (x + 6)^2 - 36

And for the y terms:
y^2 - 18y = y^2 - 18y + 81 - 81 = (y - 9)^2 - 81

Now substituting these back into the equation:
(x + 6)^2 - 36 + (y - 9)^2 - 81 + 17 = 0
(x + 6)^2 + (y - 9)^2 = 100

Now we have the equation in standard form:
(x + 6)^2 + (y - 9)^2 = 100

Comparing this to the standard form equation of a circle:
(x - h)^2 + (y - k)^2 = r^2

We can see that the center is at (-6, 9) and the radius is 10.