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JEE Main20244 Apr 2024Evening ShiftMathematicsStraight LinesActual

Consider a triangle ABC having the vertices A (1,2), B ( , ) and C ( , ) and angles A B C= 6 and B A C= 2 3 . If the points B and C lie on the line y=x+4 , then ^2+ ^2 is equal to ________

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Step-by-step solution

Equation of line passes through point A (1,2) which makes angle 6 from y=x+4 is aligned & y-2= 1 6 1 6 (x-1) & y-2= 3 1 3 1 (x-1) & array c|c & y -2=(2+ 3 )( x -1) & y -2=(2- 3 )( x -1) array & solve with y = x +4 solve with y = x +4 & x+2=(2+ 3 ) x-2- 3 x+2=(2- 3 ) x-2+ 3 & x= 4+ 3 1+ 3 x= 4- 3 1- 3 & aligned aligned & ^2+ ^2= ( 4+ 3 1+ 3 )^2+ ( 4- 3 1- 3 )^2 & ^2+ ^2=14 aligned

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