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What is the equation of a circle with center at (2, -3) and radius 5?

Practice Questions

Q1
What is the equation of a circle with center at (2, -3) and radius 5?
  1. (x - 2)² + (y + 3)² = 25
  2. (x + 2)² + (y - 3)² = 25
  3. (x - 2)² + (y - 3)² = 25
  4. (x + 2)² + (y + 3)² = 25

Questions & Step-by-Step Solutions

What is the equation of a circle with center at (2, -3) and radius 5?
  • Step 1: Identify the center of the circle, which is given as (2, -3). Here, h = 2 and k = -3.
  • Step 2: Identify the radius of the circle, which is given as 5. So, r = 5.
  • Step 3: Use the standard form of the circle's equation: (x - h)² + (y - k)² = r².
  • Step 4: Substitute h and k into the equation: (x - 2)² + (y + 3)² = r².
  • Step 5: Substitute r into the equation: (x - 2)² + (y + 3)² = 5².
  • Step 6: Calculate 5², which is 25. So, the equation becomes (x - 2)² + (y + 3)² = 25.
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