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Two normals to the parabola y² = 4x are drawn at the points (4, -4) and (9, -6). The third normal to the parabola that passes through the intersection point of these two normals is:

1. 5x + y - 135 = 0
2. 5x - y + 115 = 0
3. 5x - y - 115 = 0
4. 5x + y + 115 = 0

Correct answer: 5x + y - 135 = 0

Solution

Points (4,-4) and (9,-6) correspond to t = -2 and t = -3; concurrency requires t3 = 5, giving the normal y = -5x + 135, i.e. 5x + y - 135 = 0.

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