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Question

Find the value of 'p', if the straight lies x+p=0,y+2=0 and 3x+2y+5=0 are concurrent.


Solution

$$\begin{array}{l} x+p=0.................\left( 1 \right)  \\ y+2=0.................\left( 2 \right)  \\ 3x+2y+5=0..............\left( 3 \right)  \\ pt.\, \, of\, \, { { int } }er\sec  tion\, \, of\, \, { { lines } }\, \, \left( 2 \right) \, \, \, and\, \left( 3 \right)  \\ \left( { \frac { { -1 } }{ 3 } ,-2 } \right)  \\ -\frac { 1 }{ 3 } +p=0 \\ \Rightarrow p=\frac { 1 }{ 3 }  \end{array}$$

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