x 2 + y 2 − 4 x + 2 y + 4 = 0 is the equation of a circle with center ( h , k ) and radius r for: h = and k = and r = Graph the circle.

Answer 1

√( x - h)² + (y - k)² = r²

Let's take each part.

x² - 4x

We take half of -4 and square it, then add it to both sides.

x² - 4x + 4 = (x - 2)²

Same with y² + 2y + 1 = (y + 1)²

(x - 2)² + (y + 1)² = √(-4 + 4 + 1)²

(x - 2)² + (y + 1)² = 1²

Our center is (2,-1) and our radius is 1.