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Subject:  Precalculus

Properties of the ellipse x²/25 + y²/9 = 1

Find the center, foci and eccentricity of an ellipse.

Answer center (0, 0), foci (-4, 0), (4, 0), eccentricity 0.8

Solution

  1. Equation (x − 0)²/25 + (y − 0)²/9 = 1
  2. Center (0, 0)
  3. Orientation horizontal (major axis along x)
  4. Vertices (-5, 0), (5, 0)
  5. Co-vertices (0, -3), (0, 3)
  6. Foci c = √(25 − 9) = 4 → (-4, 0), (4, 0)
  7. Eccentricity e = c/a = 0.8
  8. Area A = π·a·b = 47.1239

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