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Locus of a point with a given sum of squared distances from fixed points

This type of question, asked 2 times: 2021 Paper 18, 26 Jul 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 18

    87
    The locus of a point, which moves such that the sum of squares of its distances from the points (0,0),(1,0),(0,1)(1,1)(0,0),(1,0),(0,1)(1,1) is 18 units, is a circle of diameter dd. Then d2d^{2} is equal to

  2. Question 2

    26 Jul 2022

    72
    A point PP moves so that the sum of squares of its distances from the points (1,2)(1,2) and (−2,1)( - 2,1) is 14. Let f(x,y)=0f(x,y) = 0 be the locus of PP, which intersects the xx-axis at the points A,BA,B and the yy-axis at the point C, D. Then the area of the quadrilateral ACBD is equal to

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