Write the equation in standard form for the circle x2+y2=12y.Submit

The given equation is x^2 + y^2 = 12y.

To write this equation in standard form for a circle, we need to complete the square for the y terms. The standard form for the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

Step 1: Rearrange the equation to group the y terms together:

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

Step 2: Complete the square for the y terms. To do this, take half of the coefficient of y, square it, and add it to both sides of the equation. Half of -12 is -6, and (-6)^2 = 36.

x^2 + y^2 - 12y + 36 = 36

Step 3: Rewrite the equation in standard form. The left side of the equation can be written as (x-0)^2 + (y-6)^2, and the right side of the equation is 36.

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

So, the equation of the circle in standard form is (x-0)^2 + (y-6)^2 = 36. This tells us that the circle is centered at (0,6) and has a radius of 6.