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Point on a curve where y changes k times as fast as x

This type of question, asked 2 times: 23 Apr 2025 S1, 13 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    23 Apr 2025 S1

    133
    A particle moves along a curve y=2x3−13y=\frac{2x^{3}- 1}{3}. The points on the curve at which the yy co-ordinate is changing 18 times the xx co-ordinate are

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  2. Question 2

    13 Apr 2026 S1

    58
    A point on the parabola y2=365xy^2 = \dfrac{36}{5}x at which the ordinate increases at thrice the rate of the abscissa is .....

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