How to Calculate the Center and Radius of a Circle with Ease

Learn how to find the center and radius of a circle using the standard form equation in this quick tutorial.

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To find the center and radius of a circle, use the standard form equation (x - h)² + (y - k)² = r². Here, (h, k) represents the center of the circle, and r is the radius. This method applies directly if you have the equation in standard form or can easily rearrange it.

FAQs & Answers

  1. What is the standard form equation of a circle? The standard form equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
  2. How can I find the center and radius if the equation is not in standard form? To find the center and radius when the equation is not in standard form, rearrange the equation into the standard form (x - h)² + (y - k)² = r² by completing the square for the x and y terms.
  3. What do (h, k) represent in the circle's equation? (h, k) represents the coordinates of the center of the circle in the standard form equation of a circle.
  4. Can you give an example of finding the center and radius of a circle from its equation? Sure! For the equation x² + y² - 4x + 6y - 7 = 0, rearranging and completing the square gives you the center (2, -3) and radius √(18), which is approximately 4.24.

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