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What is the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1?

Practice Questions

Q1
What is the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1?
  1. Ellipses
  2. Hyperbolas
  3. Parabolas
  4. Circles

Questions & Step-by-Step Solutions

What is the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1?
Correct Answer: Ellipses
  • Step 1: Identify the equation given, which is x^2/a^2 + y^2/b^2 = 1.
  • Step 2: Recognize that this equation is in the standard form of an ellipse.
  • Step 3: Understand that 'a' represents the length of the semi-major axis (the longer axis of the ellipse).
  • Step 4: Understand that 'b' represents the length of the semi-minor axis (the shorter axis of the ellipse).
  • Step 5: Conclude that the equation describes a family of ellipses, where the size and shape depend on the values of 'a' and 'b'.
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