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Normal at a point of a parabola meeting the parabola again

This type of question, asked 2 times: 2021 Paper 11, 2021 Paper 24. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 11

    61
    Let the tangent to the parabola S:y2=2xS:y^{2}= 2x at the point P(2,2)P(2,2) meet the xx-axis at QQ and normal at it meet the parabola SS at the point RR. Then the area (in sq. units) of the triangle PQRPQR is equal to:

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  2. Question 2

    2021 Paper 24

    73
    Consider the parabola with vertex (12,34)\left( \frac{1}{2},\frac{3}{4} \right) and the directrix y=12y=\frac{1}{2}. Let PP be the point where the parabola meets the line x=−12x = -\frac{1}{2}. If the normal to the parabola at PP intersects the parabola again at the point QQ, then (PQ)2(PQ)^{2} is equal to:

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