The value of $k$ such that the lines $2 x-3 y+k=0, \quad 3 x-4 y-13=0 \quad$ and $8 x-11 y-33=0$ are concurrent, is

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Aicharya · Accepted Answer

Since, the lines $ \begin{aligned} & 2 x-3 y+k=0,3 x-4 y-13=0 \ & 	ext { and } \quad 8 x-11 y-33=0 \ & 	ext { are concurrent } \ & 	herefore \quad\left|\begin{array}{ccc} 2 & -3 & k \ 3 & -4 & -13 \ 8 & -11 & -33 \end{array}ight|=0 \ & \Rightarrow \quad 2(132-143)+3(-99+104) \ & +k(-33+32)=0 \ & \Rightarrow \quad-22+15-k=0 \ & \Rightarrow \quad k=-7 \ & \end{aligned} $

The value of $k$ such that the lines $2 x-3 y+k=0, \quad 3 x-4 y-13=0 \quad$ and $8 x-11 y-33=0$ are…

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