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What is the equation of a circle with center at (0, 0) and radius 3?

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Question: What is the equation of a circle with center at (0, 0) and radius 3?

Options:

  1. x² + y² = 9
  2. x² + y² = 3
  3. x² + y² = 6
  4. x² + y² = 12

Correct Answer: x² + y² = 9

Solution: 

The standard form is (x - h)² + (y - k)² = r². Here, h=0, k=0, r=3, so the equation is x² + y² = 3² = 9.

What is the equation of a circle with center at (0, 0) and radius 3?

Practice Questions

Q1
What is the equation of a circle with center at (0, 0) and radius 3?
  1. x² + y² = 9
  2. x² + y² = 3
  3. x² + y² = 6
  4. x² + y² = 12

Questions & Step-by-Step Solutions

What is the equation of a circle with center at (0, 0) and radius 3?
Correct Answer: x² + y² = 9
  • Step 1: Identify the center of the circle. The center is given as (0, 0). This means h = 0 and k = 0.
  • Step 2: Identify the radius of the circle. The radius is given as 3, so r = 3.
  • Step 3: Write down the standard form of the 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 gives us (x - 0)² + (y - 0)² = 3².
  • Step 5: Simplify the equation. (x - 0)² becomes x² and (y - 0)² becomes y². So, we have x² + y² = 3².
  • Step 6: Calculate 3², which is 9. Therefore, the equation is x² + y² = 9.
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