Final answer:
The center of the circle is (1, 2) and the radius is 5 units.
Step-by-step explanation:
The given equation is a quadratic equation of the form at² + bt + c = 0, where a = 1, b = -2, and c = -20. To find the center and radius, we need to rewrite the equation in standard form by completing the square.
Step 1: Group the x terms and the y terms separately. x² - 2x + y² - 4y = 20
Step 2: Complete the square for the x terms and the y terms separately. x² - 2x + 1 + y² - 4y + 4 = 20 + 1 + 4
Step 3: Rewrite the equation in standard form. (x - 1)² + (y - 2)² = 25
The center of the circle is (1, 2) and the radius is 5 units.