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Find the length of the normals drawn for the point on the axis on the parabola y^2=8ax whose distance from the focus is 8a

Find the length of the normals drawn for the point on the axis on the parabola y^2=8ax whose distance from the focus is 8a

Grade:11

1 Answers

Arun
25763 Points
3 years ago
for parabola
y2 = 8a* x
eqn of normals =
x*t + y = 4at + 2at3
put (10a,0)
10at = 4at + 2at3
on solving,
t = 0, t =  – \sqrt3, t = \sqrt3
 
length of first normal = length of second normal
 = \sqrt[(4a)2 + (4a\sqrt3)2 ] = 8a    (answer)
 
i am unable to upload a picture of soltuion here. but you can simply understand how these points are plot

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