PYQ Vault

Area common to two parabolas y^2 = 4ax and x^2 = 4by

This type of question, asked 5 times: May 2021 S1, 4 May 2023 S1, 16 Apr 2026 S2, 12 May 2026 S1, 14 May 2026 S1. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    148
    The area (in sq. units) of the region bounded by the curves y2=4axy^2 = 4ax and x2=4ayx^2 = 4ay, a>0a>0 is

    Tap an option to check your answer.

  2. Question 2

    4 May 2023 S1

    140
    The area bounded between the curves y=ax2y=ax^2 and x=ay2 (a>0)x=ay^2\,(a>0) is 1 sq. units, then the value of aa is

    Tap an option to check your answer.

  3. Question 3

    16 Apr 2026 S2

    83
    The area of the region common to the parabolas 4y2=9x4y^2 = 9x and 3x2=16y3x^2 = 16y is...

    Tap an option to check your answer.

  4. Question 4

    12 May 2026 S1

    84
    The parabolas y2=4xy^2 = 4x and x2=4yx^2 = 4y divide the square region bounded by the lines x=4,y=4x = 4, y = 4 and the coordinate axes. If A1,A2,A3A1, A2, A3 are respectively the areas of these parts numbered from top to bottom, then A1:A2:A3A1 : A2 : A3 is ...

    Tap an option to check your answer.

  5. Question 5

    14 May 2026 S1

    84
    The area of the region bounded by the curves y2=9xy^2 = 9x and x2=9yx^2 = 9y

    Tap an option to check your answer.