Write the equation in standard form for the circle x2+y2–16y+8=0.Submit

The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

Given the equation x² + y² - 16y + 8 = 0, we can rewrite it to look more like the standard form.

First, group the y terms together: x² + (y² - 16y) + 8 = 0.

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

So, we add 64 to both sides: x² + (y² - 16y + 64) = -8 + 64.

This simplifies to: x² + (y - 8)² = 56.

So, the equation of the circle in standard form is x² + (y - 8)² = 56, with center at (0,8) and radius √56.