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Intercepts made on the axes by a tangent to a curve

This type of question, asked 3 times: 4 May 2023 S1, 13 Apr 2026 S2, 19 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S1

    122
    The sum of intercepts on coordinate axes made by tangent to the curve x+y=a\sqrt{x}+\sqrt{y}=\sqrt{a} is

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  2. Question 2

    13 Apr 2026 S2

    75
    If the tangent to the curve 2y3=x3+ax22y^3 = x^3 + ax^2 at the point (a,a)(a, a) cuts off intercepts α\alpha and β\beta on the coordinate axes such that α2+β2=61\alpha^2 + \beta^2 = 61, then the value of aa is

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  3. Question 3

    19 May 2026 S1

    76
    The tangent to the curve y=e2xy = e^{2x} is drawn at the point P(0,1)P(0, 1). If this tangent intersects the xx-axis at point AA and the yy-axis at point BB, then the area of △OAB\triangle OAB (where OO is the origin) in square units is:

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