PYQ Vault
EbooksTutor

Triangle formed by a homogeneous pair and a line: midpoint, median or centroid

This type of question, asked 3 times: 10 May 2023 S1, 14 May 2024 S2, 15 Apr 2026 S2. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    10 May 2023 S1

    150
    △OAB\triangle OAB is formed by the lines x2−4xy+y2=0x^2-4xy+y^2=0 and the line AB. The equation of line AB is 2x+3y−1=02x+3y-1=0. Then the equation of the median of the triangle drawn from the origin is

    Tap an option to check your answer.

  2. Question 2

    14 May 2024 S2

    129
    The centroid of the triangle formed by the lines x+3y=10x+3y=10 and 6x2+xy−y2=06x^2+xy-y^2=0 is

    Tap an option to check your answer.

  3. Question 3

    15 Apr 2026 S2

    59
    The line x+y=3x + y = 3 intersects the pair of straight lines x2−3xy+y2=0x^2 - 3xy + y^2 = 0 at points A and B. Then the co-ordinates of the mid-point of AB are

    Tap an option to check your answer.