The arithmetic mean of the ordinates of the feet of the normals from (3, 5) to the parabola y^2 = 8x is

JEE Advanced Mathematics question

The arithmetic mean of the ordinates of the feet of the normals from to the parabola is

Answer: (D)

For , . The normal with slope is y = mx - 2am - am^3 = mx - 4m - 2m^3, with foot .

It passes through if

5 = 3m - 4m - ⇒ + m + 5 = 0 .

**Book's (formal) reasoning.** The sum of the three roots is (no term), so

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Question ID VK-109030