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CGP EDU Academic Team
Published on: August 14, 2026
The tangent PT and the normal PN to the parabola y 2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whos
A
vertex is 
B
directrix is x = 0
C
latus rectum is 
D
focus is (a, 0)
Text Solution
Verified by ExpertsThe correct answer is:
A
(a,d)
Let centroid of Δ PTN is R (h. k)
∴ h = 
& k = 
⇒ 3h = 2a + a . 
⇒ 3h = 2a + 
⇒ 9k 2 = 4 a (3h – 2a)
locus of centroid is
y 2 = 
∴ vertex 
; directrix x – 
= – 
⇒ x = 
Latus rectum = 
focus 
i.e. (a, 0) Ans. A, D
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