What are the coordinates of the foci of the ellipse x^2 / 25 + y^2 / 16 = 1?
Answer and explanation
Correct answer: B. (3, 0) and (-3, 0)
- Step 1: For an ellipse with a^2 = 25 and b^2 = 16, the major axis lies along the x-axis because 25 > 16. Step 2. Focal distance c satisfies c^2 = a^2 - b^2 = 25 - 16 = 9 => c = 3. The foci are at (+/- 3, 0). Answer: (3, 0) and (-3, 0). Why not the others: The major vertices are (+/- 5, 0); the foci are internal at (+/- 3, 0).
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