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Condition for Two Lines to Be Parallel

Two lines are...

Question

Two lines are given by $(x - 2 y)^{2} + k (x - 2 y) = 0$ . The value of $k$ so that distance between them is $3$ , is

k = 0

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k = \pm 3 \sqrt{5}

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k = \pm 5^{\frac{1}{2}}

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k = 3

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Solution

The correct option is A $k = \pm 3 \sqrt{5}$
The lines $x - 2 y = 0$ and $x - 2 y + k = 0$ are parallel.
The distance between 2 lines $= ∣ ∣ ∣ ∣ \frac{k}{\sqrt{1 + (- 2)^{2}}} ∣ ∣ ∣ ∣ = 3 \Rightarrow k = \pm 3 \sqrt{5}$

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