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Tangent or normal to a curve through a given point

This type of question, asked 2 times: 14 Jun 2022, 28 Jun 2022. All 2 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    71
    If the tangent at the point (x1,y1)\left( x_{1},y_{1} \right) on the curve y=x3+3x2+5y =x^{3}+ 3x^{2}+ 5 passes through the origin, then (x1,y1)\left( x_{1},y_{1} \right) does NOT lie on the curve:

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  2. Question 2

    28 Jun 2022

    86
    Let l\mathcal{l} be a line which is normal to the curve y=2x2+x+2y = 2x^{2}+ x + 2 at a point PP on the curve. If the point Q(6,4)Q(6,4) lies on the line l\mathcal{l} and OO is origin, then the area of the triangle OPQ is equal to