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Problem
Problem
Find the locus of the point through which pass three normals to the parabola
y
2
=
4
a
x
y^2 = 4ax
y
2
=
4
a
x
such that two of them make angles
α
\alpha
α
and
β
\beta
β
respectively with the axis such that
tan
α
tan
β
=
2
\tan\alpha \tan\beta = 2
tan
α
tan
β
=
2
.
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