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Identify the family of curves represented by the equation x^2 + y^2 = r^2.

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Question: Identify the family of curves represented by the equation x^2 + y^2 = r^2.

Options:

  1. Straight lines
  2. Ellipses
  3. Circles
  4. Hyperbolas

Correct Answer: Circles

Solution: 

The equation x^2 + y^2 = r^2 represents a family of circles with varying radii \'r\'.

Identify the family of curves represented by the equation x^2 + y^2 = r^2.

Practice Questions

Q1
Identify the family of curves represented by the equation x^2 + y^2 = r^2.
  1. Straight lines
  2. Ellipses
  3. Circles
  4. Hyperbolas

Questions & Step-by-Step Solutions

Identify the family of curves represented by the equation x^2 + y^2 = r^2.
Correct Answer: Circles
  • Step 1: Understand the equation x^2 + y^2 = r^2.
  • Step 2: Recognize that this equation is in the standard form of a circle.
  • Step 3: Identify that 'r' represents the radius of the circle.
  • Step 4: Note that as 'r' changes, the size of the circle changes.
  • Step 5: Conclude that the equation represents a family of circles with different radii.
  • Circle Equation – The equation x^2 + y^2 = r^2 describes a circle centered at the origin with radius r.
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