Ver en españolWrite the equation in standard form for the circle x2+y2–20x–21=0.

The standard form of a circle's equation 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 - 20x - 21 = 0, we can rewrite it to look more like the standard form.

First, we can group the x terms and the y terms: (x² - 20x) + y² = 21.

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

(x² - 20x + 100) + y² = 21 + 100.

This simplifies to:

(x - 10)² + y² = 121.

So, the equation in standard form for the circle is (x - 10)² + y² = 121, with center at (10, 0) and radius of √121 = 11.