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AB is a chord of the parabola y² = 4ax with endpoints A(a*t1², 2a*t1) and B(a*t2², 2a*t2). For the case where AB is a normal chord (the chord is along the normal at A), what relation holds between t1 and t2?

1. t2 = -t1 - 2/t1
2. t2 = -4/t1
3. t2 = -1/t1
4. t2 = -t1 + 2

Correct answer: t2 = -t1 - 2/t1

Solution

The normal at the point with parameter t1 cuts the parabola again at the point whose parameter is -t1 - 2/t1.

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