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Question

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

A
π6
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B
π4
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C
π3
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D
2π3
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Solution

The correct option is C π3
The focus of the parabola y2=8ax is (2a,0).
So, the coordinates of the point on the axis of the parabola at a distance 8a from the focus is (10a,0).
Equation of a normal to the parabola y2=8ax is
y=mx4am2am3
Since it passes through (10a,0)
0=10am4am2am32am(3m2)=0m2=3(m0)
m=±3=tan(±π3)

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