Q.

If the normal drawn from the point on the axisof the parabola y2=8ax whose distance from thefocus is 8 a, and which is not parallel to eitheraxes, makes an angle θ with the axis of x, then θis equal to

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a

π /6

b

π /4

c

π /3

d

none of these

answer is C.

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Detailed Solution

Focus is (2a, 0), so point is P(2a+8a,0) Equationof any normal is y=mx−2(2a)m−(2a)m3. If itpasses through P(10a, 0), then6am−2am3=0⇒m=0,±3So the required angle is θ=tan−1⁡3=π/3.
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If the normal drawn from the point on the axisof the parabola y2=8ax whose distance from thefocus is 8 a, and which is not parallel to eitheraxes, makes an angle θ with the axis of x, then θis equal to