Conic Sections · Locus of centroid on parabola

Let

A

B

and

C

be the vertices of a variable right angled triangle inscribed in the parabola

y^2 = 16x

. Let the vertex

B

containing the right angle be

(4, 8)

and the locus of the centroid of

\triangle ABC

be a conic

C_0

. Then three times the length of latus rectum of

C_0

is .

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