What is the value of p ?
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. \sqrt{7}
- B. 3
- C. 7 ✓
- D. 9
Correct Answer: C. 7
Explanation
For the hyperbola, a^2 = 144/25, b^2 = 81/25, giving c^2 = 225/25 = 9. Foci are (\pm 3, 0). For the ellipse, a^2 = 16, b^2 = p, giving c^2 = 16 - p. Equating c^2 yields 16 - p = 9, so p = 7.
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