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Area bounded by a parabola, its tangent and an axis or line

This type of question, asked 4 times: 2021 Paper 21, 11 Apr 2023, 30 Jan 2024, 4 Apr 2025. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 21

    76
    The area of the region bounded by the parabola (y−2)2=(x−1)(y- 2)^{2}= (x- 1), the tangent to it at the point whose ordinate is 3 and the xx-axis is:

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  2. Question 2

    11 Apr 2023

    180
    If AA is the area in the first quadrant enclosed by the curve C:2x2−y+1=0C:2x^{2}- y + 1 = 0, the tangent to CC at the point (1,3)(1,3) and the line x+y=1x + y = 1, then the value of 60 A60\text{ }A is

  3. Question 3

    30 Jan 2024

    179
    The area of the region enclosed by the parabola (y−2)2=x−1(y- 2)^{2}=x- 1, the line x−2y+4=0x- 2y+ 4 = 0 and the positive coordinate axes is

  4. Question 4

    4 Apr 2025

    134
    A line passing through the point A(−2,0)A\left( - 2,0 \right), touches the parabola P:y2=P:y^{2}= x−2x- 2 at the point BB in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-

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