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What is the equation of a circle with center at (2, -3) and radius 4? (2022)

Practice Questions

Q1
What is the equation of a circle with center at (2, -3) and radius 4? (2022)
  1. (x-2)² + (y+3)² = 16
  2. (x+2)² + (y-3)² = 16
  3. (x-2)² + (y-3)² = 16
  4. (x+2)² + (y+3)² = 16

Questions & Step-by-Step Solutions

What is the equation of a circle with center at (2, -3) and radius 4? (2022)
  • Step 1: Identify the center of the circle. The center is given as (2, -3). Here, h = 2 and k = -3.
  • Step 2: Identify the radius of the circle. The radius is given as 4.
  • Step 3: Recall the standard form of a circle's equation, which is (x-h)² + (y-k)² = r².
  • Step 4: Substitute the values of h, k, and r into the equation. This gives us (x-2)² + (y-(-3))² = 4².
  • Step 5: Simplify the equation. Since y-(-3) is the same as y+3, we have (x-2)² + (y+3)² = 16.
  • Step 6: Write the final equation of the circle: (x-2)² + (y+3)² = 16.
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