PYQ Vault
EbooksTutor

Locus of the centroid of a triangle inscribed in a parabola

This type of question, asked 2 times: 21 Jan 2026 S2, 4 Apr 2026 S2. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    21 Jan 2026 S2

    55
    Let y2=12xy^{2}= 12x be the parabola with its vertex at O . Let P be a point on the parabola and A be a point on the x -axis such that ∠OPA=90∘\angle OPA =90^{\circ}. Then the locus of the centroid of such triangles OPA is :

    Tap an option to check your answer.

  2. Question 2

    4 Apr 2026 S2

    74
    Let A,BA,B and C be the vertices of a variable right angled triangle inscribed in the parabola y2=16xy^{2} = 16x. Let the vertex BB containing the right angle be (4,8)(4,8) and the locus of the centroid of △ABC\bigtriangleup ABC be a conic C0C_{0}. Then three times the length of latus rectum of C0C_{0} is ____\_\_\_\_ .