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The family of curves represented by the equation x^2 + y^2 = r^2 is known as:

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Question: The family of curves represented by the equation x^2 + y^2 = r^2 is known as:

Options:

  1. Ellipses
  2. Hyperbolas
  3. Circles
  4. Parabolas

Correct Answer: Circles

Solution: 

The equation x^2 + y^2 = r^2 represents a family of circles.

The family of curves represented by the equation x^2 + y^2 = r^2 is known as:

Practice Questions

Q1
The family of curves represented by the equation x^2 + y^2 = r^2 is known as:
  1. Ellipses
  2. Hyperbolas
  3. Circles
  4. Parabolas

Questions & Step-by-Step Solutions

The family of curves represented by the equation x^2 + y^2 = r^2 is known as:
  • Step 1: Understand the equation x^2 + y^2 = r^2.
  • Step 2: Recognize that this equation describes a shape in a coordinate system.
  • Step 3: Identify that 'r' represents the radius of the shape.
  • Step 4: Realize that for different values of 'r', you get different circles.
  • Step 5: Conclude that the equation represents a family of circles with varying radii.
  • Circle Equation – The equation x^2 + y^2 = r^2 describes a circle with radius r centered at the origin.
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