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Locus of a point whose distances from two fixed points are in a given ratio

The same question, asked 2 times: 2021 Paper 2*, 6 Apr 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 2

    87
    Let a point PP be such that its distance from the point (5,0)(5,0) is thrice the distance of PP from the point (−5,0)( - 5,0). If the locus of the point PP is a circle of radius rr, then 4r24r^{2} is equal to

  2. Question 2

    6 Apr 2024

    155
    If the locus of the point, whose distances from the point (2,1)(2,1) and (1,3)(1,3) are in the ratio 5:45:4, is ax2+by2+cxy+dx+ey+170=0ax^{2}+by^{2}+ cxy + dx + ey + 170 = 0, then the value of a2+2b+3c+4d+ea^{2}+ 2b + 3c + 4d + e is equal to:

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