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What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?

Practice Questions

Q1
What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?
  1. Ellipses
  2. Circles
  3. Parabolas
  4. Hyperbolas

Questions & Step-by-Step Solutions

What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?
  • Step 1: Identify the equation given: (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 semi-major axis (the longer part of the ellipse).
  • Step 4: Understand that 'b' represents the semi-minor axis (the shorter part of the ellipse).
  • Step 5: Conclude that the equation describes a family of ellipses, which can vary in size depending on the values of 'a' and 'b'.
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