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CGP EDU Academic Team
Published on: August 14, 2026
The set of pointS on the axis of the parabola y 2 = 4x + 8 from which the three normals to the parabola are all real and different is -
Text Solution
Verified by ExpertsThe correct answer is:
D
The equation of the normal at (–2 + t 2 , 2t) is
y – 2t = 
· (x + 2 – t 2 ) is
⇒ y – 2t = 
. (x + 2 – t 2 )
⇒ tx + y = 2t – 2t + t 3 ⇒ tx + y = t
3 It passes through (k, 0), if tk = t
3 .
⇒ t(t 2 – k) = 0.
It has three real values of t, if k > 0. So, the set of points (k, 0) is such that k > 0.
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