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Length of a focal chord of a parabola

This type of question, asked 4 times: 1 Feb 2023, 13 Apr 2023, 4 Apr 2024, 5 Apr 2024. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    1 Feb 2023

    173
    If the xx - intercept of a focal chord of the parabola y2=8x+4y+4y^{2}= 8x + 4y + 4 is 3 , then the length of this chord is equal to

  2. Question 2

    13 Apr 2023

    73
    Let PQPQ be a focal chord of the parabola y2=36xy^{2}= 36x of length 100, making an acute angle with the positive xx-axis. Let the ordinate of PP be positive and MM be the point on the line segment PQPQ such that PM:MQ=3:1PM:MQ = 3:1. Then which of the following points does NOT lie on the line passing through MM and perpendicular to the line PQPQ?

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  3. Question 3

    4 Apr 2024

    88
    Let the length of the focal chord PQPQ of the parabola y2=12xy^{2}= 12x be 15 units. If the distance of PQPQ from the origin is pp, then 10p210p^{2} is equal to

  4. Question 4

    5 Apr 2024

    90
    Suppose ABAB is a focal chord of the parabola y2=12xy^{2}=12x of length ll and slope m<3m<\sqrt{3}. If the distance of the chord ABAB from the origin is dd, then l d2l\,d^{2} is equal to ____