Q.

The locus of a point that is equidistant from the lines x+y−22=0 and x+y−2=0 is

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a

x+y−52=0

b

x+y−32=0

c

2x+2y−32=0

d

2x+2y−52=0

answer is C.

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Detailed 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+ c1+c22=0 ⇒x+y+-22-22=0⇒2x+2y-32=0
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The locus of a point that is equidistant from the lines x+y−22=0 and x+y−2=0 is