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Common tangent to two parabolas

This type of question, asked 2 times: 26 Jul 2022, 25 Jan 2023. All 2 questions below, oldest first.

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  1. Question 1

    26 Jul 2022

    162
    The equation of a common tangent to the parabolas y=x2y =x^{2} and y=−(x−2)2y = - (x - 2)^{2} is

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  2. Question 2

    25 Jan 2023

    62
    The distance of the point (6,−22)(6, - 2\sqrt{2}) from the common tangent y=mx+c,m>0y = mx + c,m > 0, of the curves x=2y2x = 2y^{2} and x=1+y2x = 1 +y^{2} is:

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