Question

If lines whose equation are y = 2x - 5 and 2y + px = 3 are perpendicular to each other, then the value of p is
O4
O 1
O-1
O-4

Answer 1

$y = 2x - 5 \: ---(1)$

$and \: 2y + px = 3\\ \implies 2y = -px + 3 \\\implies y = \frac{-p}{2} x + \frac{3}{2} \: ---(2)$

$\boxed{ \pink{ Slope \: of \: a \: line \: y = mx + c \: is \: m }}$

$Now, slope \: of \: y = 2x - 5 \: (m_{1}) = 2$

$Slope \: of \: second \: line (m_{2} ) = \frac{-p}{2}$

$m_{1} \times m_{2} = -1$

$\blue{( Lines \: are \: perpendicular \: to \: each \:other ) }$

$\implies 2 \times \frac{-p}{2} = -1$

$\implies -p = -1$

$\implies p = 1$

Therefore.,

$\red{Value \: of \: p} \green{ = 1}$

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