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Area between a parabola with vertical axis and a line

This type of question, asked 5 times: 2021 Paper 17, 2021 Paper 18, 7 Apr 2025, 21 Jan 2026 S2, 6 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 17

    69
    The area of the region bounded by y−x=2y-x= 2 and x2=yx^{2}= y is equal to :-

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  2. Question 2

    2021 Paper 18

    86
    The area of the region S={(x,y):3x2≤4y≤6x+24}S=\left\{ (x,y):3x^{2}\leq 4y\leq 6x+ 24 \right\} is

  3. Question 3

    7 Apr 2025

    66
    If the area of the region bounded by the curves y=4−x24y= 4 -\frac{x^{2}}{4} and y=x−42y=\frac{x- 4}{2} is equal to α\alpha, then 6α6\alpha equals.

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  4. Question 4

    21 Jan 2026 S2

    61
    If the area of the region {(x,y):1−2x≤y≤4−x2\left\{ (x,y):1 - 2x \leq y \leq 4 -x^{2} \right., x≥0,y≥0}x \geq 0,y \geq 0\} is αβ,α,β,∈N,gcd(α,β)=1\frac{\alpha}{\beta},\alpha,\beta, \in N,gcd(\alpha,\beta) = 1, then the value of (α+β)(\alpha + \beta) is :

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  5. Question 5

    6 Apr 2026 S2

    69
    The area of the region {(x,y):x2−8x≤y≤−x}\left\{ (x,y):x^{2}- 8x \leq y \leq - x \right\} is:

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