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Condition for Two Lines to Be Parallel

The distance ...

Question

The distance between the lines $5 x - 12 y + 65 = 0$ and $5 x - 12 y - 39 = 0$ is

4

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16

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2

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8

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Solution

The correct option is D $8$
The given lines are
$5 x - 12 y + 65 = 0$ .....(i)
and $5 x - 12 y - 39 = 0$ ....(ii)
Required distance $= ∣ ∣ ∣ \frac{65 + 39}{\sqrt{25 + 144}} ∣ ∣ ∣$
$(∵ d = \frac{c_{1} - c_{2}}{\sqrt{a^{2} + b^{2}}})$
$= ∣ ∣ ∣ \frac{104}{13} ∣ ∣ ∣ = 8 u n i t$

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2 {tan}^{- 1} (5 / 12)

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