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JEE Main20249 Apr 2024Evening ShiftMathematicsStraight LinesActual

Two vertices of a triangle ABC are A (3,-1) and B (-2,3) , and its orthocentre is P (1,1) . If the coordinates of the point C are ( , ) and the centre of the of the circle circumscribing the triangle PAB is ( h , k ) , then the value of ( + )+2( ~h + k ) equals

Options

  1. A5
  2. B81
  3. C15
  4. D51

Correct answer

A. 5

Step-by-step solution

M _ AB = 4 -5 M _ DP = 5 4 Equation of PC is y -1= 5 4 ( x -1) (1) M _ AP = 2 -2 =-1 M _ BC =+1 Equation of BC is y -3=( x +2) (2) On solving (1) and (2) aligned & x+4= 5 4 (x-1) 4 x+16=5 x-5 =21 & =y=x+5=26 & + =47 aligned Equation of bisector of AP y-0=(x-2) (3) Equation of bisector of AB y-1= 5 4 (x- 1 2 ) (4) aligned & On solving (3) & (4) & ( x -3) 4=5 x - 5 2 & x = -19 2 = h & y = -23 2 = k & 2( ~h + k )=-42 aligned

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