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Find the Center and Radius x^2+y^2-2x-4y-20=0

User Johndpope
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1 Answer

7 votes

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.

User BlueBadger
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