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Tangent to a parabola with a given slope

This type of question, asked 2 times: 2021 Paper 3, 5 Apr 2024. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 3

    69
    A tangent is drawn to the parabola y2=6xy^{2}= 6x which is perpendicular to the line 2x+y=12x+y= 1. Which of the following points does NOT lie on it?

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  2. Question 2

    5 Apr 2024

    179
    Let a line perpendicular to the line 2x−y=102x - y = 10 touch the parabola y2=4(x−9)y^{2}= 4(x - 9) at the point PP. The distance of the point PP from the centre of the circle x2+y2−14x−8y+56=0x^{2}+y^{2}- 14x - 8y + 56 = 0 is