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

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Question: What is the equation of the circle with center (2, -3) and radius 4?

Options:

  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

Correct Answer: (x-2)² + (y+3)² = 16

Solution: 

Equation of circle: (x-h)² + (y-k)² = r² => (x-2)² + (y+3)² = 4² = 16.

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

Practice Questions

Q1
What is the equation of the circle with center (2, -3) and radius 4?
  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 the circle with center (2, -3) and radius 4?
Correct Answer: (x-2)² + (y+3)² = 16
  • 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: Write the general equation of a circle. The equation 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: Calculate 4², which is 16. So, the equation becomes (x - 2)² + (y + 3)² = 16.
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