rite the equation in standard form for the circle y2=–x2+16x–28.Submit

The given equation is y^2 = -x^2 + 16x - 28.

To write this in standard form for a circle, we need to complete the square for the x terms. The standard form for 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.

First, let's rewrite the equation as x^2 - 16x + y^2 = 28.

To complete the square for the x terms, we take half of the coefficient of x, square it, and add it to both sides of the equation. Half of -16 is -8, and (-8)^2 = 64.

So, we add 64 to both sides of the equation to get x^2 - 16x + 64 + y^2 = 28 + 64.

This simplifies to (x - 8)^2 + y^2 = 92.

So, the equation of the circle in standard form is (x - 8)^2 + y^2 = 92. The center of the circle is at (8, 0) and the radius is sqrt(92).