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From points on the line x - y + 3 = 0, pairs of tangents are drawn to the parabola y² = 8x. The chords of contact all pass through a fixed point. Find its coordinates.

1. (3, 4)
2. (3, 2)
3. (2, 4)
4. (4, 1)

Correct answer: (3, 4)

Solution

The chord of contact from a point (h,k) on the line is k*y = 4(x + h) with h = k - 3; written as a pencil in the parameter k, the fixed point is (3, 4).

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