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Three normals are drawn to the parabola y² = 4x from the point (c, 0) on its axis. If two of these normals are perpendicular to each other, find the value of c.
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Correct answer: 3
Solution
Passing the normal through (c, 0) gives t(t² + 2 - c) = 0; the two non-axial normals satisfy t² = c - 2 with product of roots t1*t2 = (2 - c). Setting the product of their slopes equal to -1 gives c = 3.
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