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A tangent line to the ellipse x²/9 + y²/4 = 1 (centre C) meets the director circle of the ellipse at the points P and Q. Find the product of the slopes of CP and CQ.

1. -4/9
2. 9/4
3. 2/9
4. -1/4

Correct answer: -4/9

Solution

Homogenizing the circle equation with the tangent line gives a pair of lines CP, CQ whose slope product comes from the coefficients.

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