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9.Straight Line
easy
The locus of a point so that sum of its distance from two given perpendicular lines is equal to $2$ unit in first quadrant, is
A
$x + y + 2 = 0$
B
$x + y = 2$
C
$x - y = 2$
D
None of these
Solution
(b) We take the coordinate axes as two perpendicular lines. Let $P\,({x_1},{y_1})$ be the required point.
From $P\,({x_1},{y_1})$, we draw $PM$ and $PN$ perpendicular to $OX$ and $OY$ respectively.
Given, $PM + PN = 2$ ……$(i)$
But, $PM = {y_1},PN = {x_1}$
Hence from $(i)$, ${y_1} + {x_1} = 2$
Thus locus of $({x_1},{y_1})$is $x + y = 2$
which is a straight line.
Standard 11
Mathematics
