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Chords of the ellipse x²/16 + y²/25 = 1 are drawn through the point P(0, 5). The locus of their midpoints is another ellipse E. Find the coordinates of the foci of E.
- (0, 11/2) and (0, -1/2)
- (0, 3/5) and (0, -3/5)
- (0, -4) and (0, 1)
- (0, 4) and (0, 1)
Correct answer: (0, 11/2) and (0, -1/2)
Solution
The midpoint locus is x²/16 + y²/25 = y/5. Completing the square gives an ellipse centred at (0, 5/2). Its foci come out at (0, 11/2) and (0, -1/2).
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