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What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?

Practice Questions

Q1
What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?
  1. 4
  2. 8
  3. 2
  4. 16

Questions & Step-by-Step Solutions

What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?
  • Step 1: Identify the equation of the circle, which is (x - 1)² + (y + 4)² = 16.
  • Step 2: Recognize that the general form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
  • Step 3: In our equation, the right side is 16, which represents r².
  • Step 4: To find the radius (r), take the square root of 16.
  • Step 5: Calculate the square root of 16, which is 4.
  • Step 6: Conclude that the radius of the circle is 4.
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