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Normal to a curve parallel to a given line

This type of question, asked 2 times: 2021 Paper 5, 30 Jan 2023. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 5

    87
    If the normal to the curve y(x)=∫0x(2t2−15t+10)dty(x) =\int_{0}^{x} \left( 2t^{2}- 15t+ 10 \right)dt at a point (a,b)(a,b) is parallel to the line x+3y=−5,a>1x+ 3y= - 5,a> 1, then the value of ∣a+6b∣|a+ 6b| is equal to

  2. Question 2

    30 Jan 2023

    68
    The number of points on the curve y=54x5−135x4−70x3+180x2+210xy = 54x^{5}- 135x^{4}- 70x^{3}+ 180x^{2}+ 210x at which the normal lines are parallel to x+90y+2=0x + 90y + 2 = 0 is :

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