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What is the equation of a circle with center at (3, -2) and radius 4? (2023)

Practice Questions

Q1
What is the equation of a circle with center at (3, -2) and radius 4? (2023)
  1. (x-3)² + (y+2)² = 16
  2. (x+3)² + (y-2)² = 16
  3. (x-3)² + (y-2)² = 16
  4. (x+3)² + (y+2)² = 16

Questions & Step-by-Step Solutions

What is the equation of a circle with center at (3, -2) and radius 4? (2023)
  • Step 1: Identify the center of the circle. The center is given as (3, -2). Here, h = 3 and k = -2.
  • Step 2: Identify the radius of the circle. The radius is given as 4.
  • Step 3: Recall the standard equation of a circle, which is (x - h)² + (y - k)² = r².
  • Step 4: Substitute the values of h, k, and r into the equation. This means replacing h with 3, k with -2, and r with 4.
  • Step 5: The equation becomes (x - 3)² + (y - (-2))² = 4².
  • Step 6: Simplify the equation. Since y - (-2) is the same as y + 2, the equation is (x - 3)² + (y + 2)² = 16.
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