Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Three normals are drawn to the parabola y 2 = 4x from the point (c, 0). These normals are real and distinct when -
Text Solution
Verified by ExpertsThe correct answer is:
D
Any point on y 2 = 4x is (t 2 , 2t). Since 
= 
so 
= 
= 
. Hence equation of normal at (t 2 , t) is
Y – 2t = –t (X – t 2 )
This passes through (c, 0) if –2t = – t (c – t 2 )
⇒ t = 0, t 2 = c – 2
Thus the roots are real and distinct if c > 2
so c = 3 is the correct choice.
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