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CGP EDU Academic Team
Published on: August 13, 2026
Normals are drawn from the point P on a parabola y 2 = 4x with slopes m 1 . m 2 = α is a part of the parabola it self, then the value of α is.
Text Solution
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2
Ans. 2
Sol.
Let the point P be (h, k)
equation of normal k = mh – 2m – m 3 m
3 + m (2 – h) + k = 0
m 1 m 2 m 3 = – k ⇒ m 3 = 
[ Q m 1 m 2 = α ] 
(2 – h) + k = 0
k 2 = α 2 h – 2 α 2 + α 3 locus of (h, k) is
y
2 = α 2 x – 2 α 2 + α 3 compare with y
2 = 4x we get
α 2 = 4 & – 2 α 2 + α 3 = 0
⇒ α = 2
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