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What is the equation of a circle with center at (h, k) and radius r?

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Question: What is the equation of a circle with center at (h, k) and radius r?

Options:

  1. (x - h)^2 + (y - k)^2 = r^2
  2. (x + h)^2 + (y + k)^2 = r^2
  3. (x - h)^2 - (y - k)^2 = r^2
  4. (x + h)^2 - (y + k)^2 = r^2

Correct Answer: (x - h)^2 + (y - k)^2 = r^2

Solution: 

The equation of a circle with center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

What is the equation of a circle with center at (h, k) and radius r?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the equation of a circle with center at (h, k) and radius r?
  • Step 1: Identify the center of the circle, which is given as (h, k). This means 'h' is the x-coordinate and 'k' is the y-coordinate of the center.
  • Step 2: Identify the radius of the circle, which is given as 'r'. This is the distance from the center to any point on the circle.
  • Step 3: The general formula for the equation of a circle is based on the distance from the center to any point (x, y) on the circle.
  • Step 4: To express this mathematically, we use the formula: (x - h)^2 + (y - k)^2 = r^2.
  • Step 5: In this formula, (x - h) represents the horizontal distance from the center to the point (x, y), and (y - k) represents the vertical distance.
  • Step 6: Squaring these distances and adding them together gives us the equation of the circle.
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