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If the normal drawn from the point on the axis
of the parabola $y^{2} = 8 a x$ whose distance from the
focus is 8 $a,$ and which is not parallel to either
axes, makes an angle $θ$ with the axis of $x,$ then $θ$
is equal to

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π /6

π /4

π /3

none of these

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detailed solution

Correct option is C

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

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Ready to Test Your Skills?

free study material

If the normal drawn from the point on the axis
of the parabola $y^{2} = 8 a x$ whose distance from the
focus is 8 $a,$ and which is not parallel to either
axes, makes an angle $θ$ with the axis of $x,$ then $θ$
is equal to