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The value of 'K' such that line $3 x + 4 y + 5 - k (x + y + 3) = 0$ parallel to $Y -$ axis is

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answer is D.

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Detailed Solution

$\begin{array}{l} 3 x + 4 y + 5 - k (x + y + 3) = 0 \\ 3 x + 4 y + 5 - k x - k y - 3 k = 0 \\ (3 - k) x + (4 - k) y + (5 - 3 k) = 0 \end{array}$

Slope of parallel to $Y -$ axis is undefined

$\begin{array}{l} \frac{- (3 - k)}{4 - k} = \frac{1}{0} \\ \Rightarrow 4 - k = 0 \\ ∴ k = 4 \end{array}$

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