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Triangle with sides 2x + y = 0, x + py = k and x - y = 3 and one of its centres given

This type of question, asked 3 times: 26 Jul 2022, 27 Jul 2022, 24 Jan 2023. All 3 questions below, oldest first.

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  1. Question 1

    26 Jul 2022

    88
    The equations of the sides AB,BCAB,BC and CACA of a triangle ABCABC are 2x+y=0,x+py=15a2x+y= 0,x+py= 15a and x−y=3x-y= 3 respectively. If its ortho centre is (2,a)(2,a), −12<a<2-\frac{1}{2}< a < 2, then pp is equal to

  2. Question 2

    27 Jul 2022

    161
    The equations of the sides AB,BCAB,BC and CACA of a triangle ABCABC are 2x+y=0,x+py=392x + y = 0,x + py = 39 and x−y=3x - y = 3 respectively and P(2,3)P(2,3) is its circumcentre. Then which of the following is NOT true:

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  3. Question 3

    24 Jan 2023

    176
    The equations of the sides AB,BCAB,BC and CACA of a triangle ABCABC are: 2x+y=0,x+py=21a,(a≠0)2x + y = 0,x + py = 21a,(a \neq 0) and x−y=3x - y = 3 respectively. Let P(2,a)P(2,a) be the centroid of △ABC\bigtriangleup ABC. Then (BC)2(BC)^{2} is equal to