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Which of the following equations represents a circle with a center at (0, 0) and

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Question: Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?

Options:

  1. x^2 + y^2 = 5
  2. x^2 + y^2 = 25
  3. x^2 - y^2 = 25
  4. x^2 + y^2 = 10

Correct Answer: x^2 + y^2 = 25

Solution:

The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.

Which of the following equations represents a circle with a center at (0, 0) and

Practice Questions

Q1
Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?
  1. x^2 + y^2 = 5
  2. x^2 + y^2 = 25
  3. x^2 - y^2 = 25
  4. x^2 + y^2 = 10

Questions & Step-by-Step Solutions

Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?
  • Step 1: Understand that the standard equation of a circle with center at (0, 0) is x^2 + y^2 = r^2.
  • Step 2: Identify the radius of the circle, which is given as 5.
  • Step 3: Calculate r^2 by squaring the radius: 5^2 = 25.
  • Step 4: Substitute r^2 into the standard equation: x^2 + y^2 = 25.
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