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Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

Two straight ...

Question

Two straight lines $x + 2 y = 2$ and $x + 2 y = 6$ are given, then find the equation of the line parallel to given lines and divided distance between lines in the ratio $2 : 1$ internally.

3 x + 6 y + 8 = 0

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3 x + 4 y = 14

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3 x + 6 y = 14

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3 x + 2 y = 10

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Solution

The correct option is B $3 x + 6 y = 14$
distance between the two lines $x + 2 y = 2, x + 2 y = 6$ is $6 - 2 = 4$
distance of required line from x+2{y}=2 is $4 \times \frac{2}{3} = \frac{8}{3}$
$⟹$ the required line is $x + 2 y = 2 + \frac{8}{3} ⟹ 3 x + 6 y = 14$

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