First slide

Equation of line in Straight lines

Question

The locus of a point that is equidistant from the lines $x + y - 2 \sqrt{2} = 0 and x + y - \sqrt{2} = 0 is$

Moderate

A

$x + y - 5 \sqrt{2} = 0$
B

$x + y - 3 \sqrt{2} = 0$
C

$2 x + 2 y - 3 \sqrt{2} = 0$
D

$2 x + 2 y - 5 \sqrt{2} = 0$

Solution

For any point P(x, y) that is equidistant from the given line,
given lines are parallel , so the required line is ax+by+ $\frac{c_{1} + c_{2}}{2}$ =0
$\Rightarrow x + y + (\frac{- 2 \sqrt{2} - \sqrt{2}}{2}) = 0 \Rightarrow 2 x + 2 y - 3 \sqrt{2} = 0$

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