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What is the equation of a circle with center at (-1, 2) and radius 4?

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Question: What is the equation of a circle with center at (-1, 2) and radius 4?

Options:

  1. (x + 1)² + (y - 2)² = 16
  2. (x - 1)² + (y + 2)² = 16
  3. (x + 1)² + (y + 2)² = 16
  4. (x - 1)² + (y - 2)² = 16

Correct Answer: (x + 1)² + (y - 2)² = 16

Solution: 

Using the standard form, the equation is (x + 1)² + (y - 2)² = 4² = 16.

What is the equation of a circle with center at (-1, 2) and radius 4?

Practice Questions

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

Questions & Step-by-Step Solutions

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