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Area between a circle and a parabola

This type of question, asked 8 times: 2021 Paper 1, 27 Jul 2022, 29 Jan 2023, 10 Apr 2023, 11 Apr 2023, 8 Apr 2024, 9 Apr 2024, 22 Jan 2025. All 8 questions below, oldest first.

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  1. Question 1

    2021 Paper 1

    73
    The area (in sq. units) of the part of the circle x2+y2=36x^{2}+y^{2}= 36, which is outside the parabola y2=9xy^{2}= 9x, is:

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  2. Question 2

    27 Jul 2022

    69
    The area of the smaller region enclosed by the curves y2=8x+4y^{2}= 8x + 4 and x2+y2+43x−4=0x^{2}+y^{2}+ 4\sqrt{3}x - 4 = 0 is equal to

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  3. Question 3

    29 Jan 2023

    73
    Let Δ\Delta be the area of the region {(x,y)∈R2:x2+y2≤21,y2≤4x,x≥1}\left\{ (x,y) \in R^{2}:x^{2}+y^{2}\leq 21,y^{2}\leq 4x,x \geq 1 \right\}. Then 12(Δ−21sin⁡−127)\frac{1}{2}\left( \Delta - 21\sin^{- 1}\frac{2}{\sqrt{7}} \right) is equal to

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  4. Question 4

    10 Apr 2023

    87
    Let y=p(x)y = p(x) be the parabola passing through the points (−1,0),(0,1)( - 1,0),(0,1) and (1,0)(1,0). If the area of the region {(x,y):(x+1)2+(y−1)2≤1,y≤p(x)}\left\{ (x,y):(x + 1)^{2}+ (y - 1)^{2}\leq 1,y \leq p(x) \right\} is AA, then 12(π−4 A)12(\pi - 4\text{ }A) is equal to

  5. Question 5

    11 Apr 2023

    73
    Area of the region {(x,y):x2+(y−2)2≤4\left\{ (x,y):x^{2}+ (y - 2)^{2}\leq 4 \right.,  x2≥2y}\left. \ x^{2}\geq 2y \right\} is

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  6. Question 6

    8 Apr 2024

    161
    The area of the region in the first quadrant inside the circle x2+y2=8x^{2}+y^{2}= 8 and outside the parabola y2=2xy^{2}= 2x is equal to :

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  7. Question 7

    9 Apr 2024

    62
    The parabola y2=4xy^{2}= 4x divides the area of the circle x2+y2=5x^{2}+y^{2}= 5 in two parts. The area of the smaller part is equal to :

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  8. Question 8

    22 Jan 2025

    68
    The area of the region, inside the circle (x−23)2+y2=12(x - 2\sqrt{3})^{2}+y^{2}= 12 and outside the parabola y2=23xy^{2}= 2\sqrt{3}x is

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