What is the difference between the eccentricities of the hyperbola and the ellipse ?

For the next two (02) items that follow : The foci of the ellipse \( px^2 + 16y^2 = 16p \) and the foci of the hyperbola \( 25(81x^2 - 144y^2) = 11664 \) coincide (assume p < 16).

  1. A. 0.5
  2. B. 0.75
  3. C. 1.0
  4. D. 1.25

Correct Answer: A. 0.5

Explanation

The hyperbola's eccentricity is c/a = 3 / (12/5) = 1.25. The ellipse's eccentricity is c/a = 3 / 4 = 0.75. The difference is 1.25 - 0.75 = 0.5.

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