Find the equation of two straight lines each of which is parallel to and at a distance of 5 from the line x + 2y - 7 = 0.
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The equation of any line parallel to
x+2y−7=0
x+2y−7=0
is x+2y+k=0
The distance between these two lines is:
d=|k+7|5–√d
=|k+7|5
Put d=5–√d=5 ,
–√5=|k+7|5–√5
=|k+7|5
5=|k+7|
k+7=5 (or) k+7=−5
k=−2 (or) k=−12
Hence the equations of the two lines are x+2y−2=0x+2y−2=0 and x+2y−12=0
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