JEE Main20253 Apr 2025Evening ShiftMathematicsStraight LinesActual

Let the equation x ( x +2)(12- k )=2 have equal roots. Then the distance of the point ( k , k 2 ) from the line 3 x+4 y+5=0 is

Options

A15
B5 3
C15 5
D12

Correct answer

A. 15

Step-by-step solution

aligned & ( x ^2+2 x )(12- k )=2 & x ^2+2 x -2=0 k 12 Let 12- k = & D =0 & 4 ^2+8 =0 & =0 or =-2 & 12- k =-2 & k =14 aligned So P (k, k 2 )=(14,7) d = | 3 14+4 7+5 5 |=15 option (1)

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