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Radius of the largest circle centred at (2, 0) that fits inside an ellipse

The same question, asked 2 times: 24 Jan 2023*, 11 Apr 2023. Every wording below, oldest first.

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  1. Question 1

    24 Jan 2023

    89
    Let CC be the largest circle centred at (2,0)(2,0) and inscribed in the ellipse x236+y216=1\frac{x^{2}}{36}+\frac{y^{2}}{16}= 1. If (1,α)(1,\alpha) lies on CC, then 10α210\alpha^{2} is equal to

  2. Question 2

    11 Apr 2023

    164
    If the radius of the largest circle with centre (2,0)(2,0) inscribed in the ellipse x2+4y2=36x^{2}+ 4y^{2}= 36 is rr, then 12r212r^{2} is equal to

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