Write the equation in standard form for the circle y2+41=–x2–18x.Submit

The given equation is y^2 + 41 = -x^2 - 18x.

First, let's rearrange the equation to get the x terms on one side and the y terms on the other:

x^2 + 18x + y^2 = -41

Next, we want to complete the square for the x terms. To do this, we take half of the coefficient of x, square it, and add it to both sides. Half of 18 is 9, and 9 squared is 81.

x^2 + 18x + 81 + y^2 = -41 + 81

This simplifies to:

(x + 9)^2 + y^2 = 40

This is the standard form of the equation for a circle, where the center is at (-9, 0) and the radius is the square root of 40, or 2*sqrt(10).