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Locus of a point making a triangle of given area with two fixed points

This type of question, asked 2 times: 2021 Paper 23, 5 Apr 2024. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 23

    76
    Let AA be the set of all points (α,β)(\alpha,\beta) such that the area of triangle formed by the points (5,6),(3,2)(5,6),(3,2) and (α,β)(\alpha,\beta) is 12 square units. Then the least possible length of a line segment joining the origin to a point in AA, is:

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  2. Question 2

    5 Apr 2024

    158
    Let A(−1,1)A( - 1,1) and B(2,3)B(2,3) be two points and PP be a variable point above the line ABAB such that the area of △PAB\bigtriangleup PAB is 10. If the locus of PP is ax+by=15ax + by = 15, then 5a+2b5a + 2b is:

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