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The straight line 3x + 2y + 1 = 0 intersects the hyperbola 4x² - y² = 4a² at points P and Q. The point where the tangents drawn to the hyperbola at P and Q intersect is

1. (-3a², 8a²)
2. (3a², 8a²)
3. (3a², -8a²)
4. None of these

Correct answer: (-3a², 8a²)

Solution

For x^2/a^2 - y^2/4a^2 = 1, the chord of contact from (x1,y1) is 4x1 x - y1 y = 4a^2. Matching with 3x+2y+1=0 gives x1=-3a^2, y1=8a^2, so the point is (-3a^2, 8a^2).

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