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From the external point P(3, 4), tangents are drawn to the ellipse x²/9 + y²/4 = 1, touching it at points A and B. Find the coordinates of A and B.
- (3, 0) and (-9/5, 8/5)
- (3, 0) and (0, 2)
- (-8/5, 2*sqrt(261)/15) and (9/5, 8/5)
- (-8/5, 2*sqrt(161)/15) and (0, 2)
Correct answer: (3, 0) and (-9/5, 8/5)
Solution
The chord of contact x/3 + y = 1 meets the ellipse at (3, 0) and (-9/5, 8/5).
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