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Question

The locus of point P when three normals drawn from it to parabola y2=4ax are such that two of them make complementary angles is

A
y2=a(xa)
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B
y2=xa
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C
x2=a(ya)
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D
x2=ya
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Solution

The correct option is A y2=a(xa)
Eqaution of normal to y2=4ax passing through P whose locus is (h,k) is
k=mh2amam3
am3+(2ah)m+k=0 (1)
It has 3 roots.
m1m2m3=ka
As 2 tangents make complementary angles,
so if m1=tanθ, then m2=cotθ
m3=ka
Putting this in equation (1),
a(ka)3+(2ah)(ka)+k=0
By solving, we get
k2=aha2
y2=a(xa)

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