Let PQ be a variable focal chord of the parabola y 2 = 4ax where vertex is A. Locus of, centroid of triangle APQ is a parabola ‘P 1 ’
(i) Latus rectum of parabola P 1 is
Text Solution
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(i) If (x, y) is the centroid of triangle formed by A(0, 0), P(t) and Q 
is
3x = a 
3y = 2a 
Eliminating t we get
9y 2 = 4a(3x – 2a) or y 2 = 
∴ length of latus rectum is 
(ii) Since y 2 = 
is the equation of parabola P 1 hence vertex is 
(iii) using property
Δ 1 = 2 Δ 2
directrix of P 1 is
x – 
= 
i.e. x = a/3 as orthocentre of T lies on the directrix of P 1
∴ orthocentre of T lies on x = 
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