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).
- A. 0.5 ✓
- B. 0.75
- C. 1.0
- 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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