Write the equation in standard form for the circle x2+y2–20y+20=0.Submit

The given equation is x^2 + y^2 - 20y + 20 = 0.

To write this equation in standard form for a circle, we need to complete the square for the y 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.

Step 1: Group the y terms together: x^2 + (y^2 - 20y) + 20 = 0.

Step 2: To complete the square, we take half of the coefficient of y, square it and add it to both sides of the equation. Half of -20 is -10, and (-10)^2 = 100. So, we add 100 to both sides: x^2 + (y^2 - 20y + 100) = -20 + 100.

Step 3: Simplify the equation: x^2 + (y - 10)^2 = 80.

So, the equation in standard form for the given circle is x^2 + (y - 10)^2 = 80. The center of the circle is at (0, 10) and the radius is sqrt(80) or approximately 8.94.