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Circles touching both coordinate axes

This type of question, asked 2 times: 6 Apr 2023, 12 Apr 2023. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    6 Apr 2023

    82
    A circle passing through the point P(α,β)P(\alpha,\beta) in the first quadrant touches the two coordinate axes at the points AA and BB. The point PP is above the line ABAB. The point QQ on the line segment ABAB is the foot of perpendicular from PP on ABAB. If PQPQ is equal to 11 units, then the value of αβ\alpha\beta is

  2. Question 2

    12 Apr 2023

    90
    Two circles in the first quadrant of radii r1r_{1} and r2r_{2} touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x+y=2x + y = 2. Then r12+r22−r1r2r_{1}^{2}+r_{2}^{2}-r_{1}r_{2} is equal to