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What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?

Practice Questions

Q1
What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
  1. 7
  2. 8
  3. 9
  4. 10

Questions & Step-by-Step Solutions

What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
  • Step 1: Identify the equation of the ellipse, which is x^2/25 + y^2/16 = 1.
  • Step 2: Recognize that this is in the standard form of an ellipse, where a^2 = 25 and b^2 = 16.
  • Step 3: Calculate 'a' by taking the square root of a^2: a = √25 = 5.
  • Step 4: Calculate 'b' by taking the square root of b^2: b = √16 = 4.
  • Step 5: Use the formula to find 'c', where c = √(a^2 - b^2).
  • Step 6: Substitute the values: c = √(25 - 16) = √9 = 3.
  • Step 7: The distance between the foci is given by 2c, so calculate 2c = 2 * 3 = 6.
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