If the sum of squares of all real values of , for which the lines 2x-y+3=0 ,6x+3y+1=0 and αx+2y-2=0 do not form a triangle is p, then the greatest integer less than or equal to p is

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Accepted Answer

Correct answer: 32. (32) 2x-y+3=06x+3y+1=0 αx+2y-2=0 Will not form a if αx+2y-2=0 is concurrent with 2x-y+3=0 and 6x+3y+1=0 or parallel to either of them so Case-1: Concurrent lines (2-13631 2-2)=0 ⇒ = 45 Case-2 : Parallel lines- 2= -63 or- 2=2 ⇒ =4 or =-4 ⇒=16+16+ 1625 [P ]=(32+ 1625)=32

$If the sum of squares of all real values of α, for which the lines 2 x - y + 3 = 0, 6 x + 3 y + 1 = 0 and αx + 2 y - 2 = 0 do not form a triangle is p, then the greatest integer less than or equal to p is$

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