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Area cut from a circle by a line or by y = |x - a|

This type of question, asked 4 times: 29 Jul 2022, 29 Jan 2023, 29 Jan 2024, 23 Jan 2025. All 4 questions below, oldest first.

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  1. Question 1

    29 Jul 2022

    76
    The area of the region {(x,y):∣x−1∣≤y≤5−x2}\left\{ (x,y):|x - 1| \leq y \leq\sqrt{5 -x^{2}} \right\} is equal to :

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  2. Question 2

    29 Jan 2023

    75
    Let A={(x,y)∈R2:y≥0,2x≤y≤4−(x−1)2}A =\left\{ (x,y) \in R^{2}:y \geq 0,2x \leq y \leq\sqrt{4 - (x - 1)^{2}} \right\} and
    B={(x,y)∈R×R:0≤y≤min{2x,4−(x−1)2}}B =\left\{ (x,y) \in R \times R:0 \leq y \leq min\left\{ 2x,\sqrt{4 - (x - 1)^{2}} \right\} \right\}
    Then the ratio of the area of AA to the area of BB is

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  3. Question 3

    29 Jan 2024

    88
    The area (in sq. units) of the part of circle x2+y2=169x^{2}+y^{2}= 169 which is below the line 5x−y=135x-y= 13 is πα2β−652+αβsin⁡−1(1213)\frac{\pi\alpha}{2\beta}-\frac{65}{2}+\frac{\alpha}{\beta}\sin^{- 1}\left( \frac{12}{13} \right) where α,β\alpha,\beta are coprime numbers. Then α+β\alpha+\beta is equal to

  4. Question 4

    23 Jan 2025

    71
    If the area of the larger portion bounded between the curves x2+y2=25x^{2}+y^{2}= 25 and y=∣x−1∣y = |x - 1| is 14(bπ+c)\frac{1}{4}(b\pi + c), b,c∈Nb,c \in N, then b+cb + c is equal to ___\_\_\_