Find locus of a point P if the three normals drawn from it to the parabola y 2 = 4ax are such that two of them make complementry angles with the axis of the parabola
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
y 2 = a (x − a)
Sol. Let point P be (h, k). equation of normal
y = mx – 2am – am 3
k = mh – 2a.m – am 3
am 3 + m(2a – h) + k = 0 ........(1)
m 1 + m 2 + m 3 = 0
= 
m 1 m 2 m 3 = – 
given m 1 m 2 = 1 as if m 1 = tan θ , then m 2 = tan (90 – θ ) = cot θ
m 3 = – 
in equation ........(2)
putting (2) in (1)
– 
– 
(2a – h) + k = 0
⇒ – 
(k 2 + a(2a – h) – a 2 ) = 0 ( k ≠ 0)
y 2 = a(x – a)
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