Calculate the center of the circle by completing the square of the equation x2+y2−6x−12y+5=0

Question

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Answer 1

To find the center of the circle by completing the square, we need to rewrite the equation of the circle in the standard form:

x^2 - 6x + y^2 - 12y + 5 = 0

First, let's complete the square for the x terms:

x^2 - 6x = (x - 3)^2 - 9

Next, let's complete the square for the y terms:

y^2 - 12y = (y - 6)^2 - 36

Now, let's substitute these into the equation:

(x - 3)^2 - 9 + (y - 6)^2 - 36 + 5 = 0

(x - 3)^2 + (y - 6)^2 = 40

Now the equation is in standard form:

(x - h)^2 + (y - k)^2 = r^2

So, the center of the circle is at (3, 6) and the radius of the circle is sqrt(40) = 2(sqrt(10)).