Question

Complete the second step in writing the equations of a circle in graphing form. EQUATION: x^2-2x+y^2+6y-6=0 STEP 1: x^2-2x+y^2+6y=6 STEP 2: x^2-2x+[1]+y^2+6y+9=6+1+9

Answer 1

EQUATION: x^2 - 2x + y^2 + 6y - 6 = 0

STEP 1: x^2 - 2x + y^2 + 6y = 6

STEP 2: x^2 - 2x + [1] + y^2 + 6y + 9 = 6 + 1 + 9

So far you are correct. Now you have to factor the quadratic in x and the quadratic in y.

(x - 1)^2 + (y + 3)^2 = 16

(x - 1)^2 + (y + 3)^2 = 4^2

Compare your equation with the standard equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

Your circle is centered at (1, -3) and radius 4.