x² + 2x + y² + 4y = 20
We complete the square in both x and y. For each we add half the linear coefficient, squared. So (2/2)²=1 for x and (4/2)²=4 for y. We add them to both sides to keep the equation the same.
x² + 2x + 1 + y² + 4y + 4 = 20 + 1 + 4
Now the left side is the sum of squares and the right side is the squared radius.
(x + 1)² + (y + 2)² = 5²
Standard form is (x-p)² + (y-q)² = r² for center (p,q) and radius r. Note the minus signs.
We read off the answer:
Answer: Center (-1, -2), radius 5.
