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Terms in an Arithmetic Progression

The arithmeti...

Question

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

A

4

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B

0

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C

8

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D

none of these

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Solution

The correct option is B $0$
We know the relation between the feet of normals to the parabola
as $y_{1} + y_{2} + y_{3} = 0$
Hence required arithmetic mean of the ordinates $= \frac{y_{1} + y_{2} + y_{3}}{3} = 0$

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