Find the equation of a straight line passing through the point `(-5,4)` and which cuts off an intercept of `sqrt(2)` units between the lines `x+y+1=0`

Question

Find the equation of a straight line passing through the point `(-5,4)` and which cuts off an intercept of `sqrt(2)` units between the lines `x+y+1=0`

Find the equation of a straight line passing through the point `(-5,4)` and which cuts off an intercept of `sqrt(2)` units between the lines `x+y+1=0` and `x+y-1=0.`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - x-y+9=0
Since the perpendicular distance between the given lines is `sqrt(2)`, the required line is a straight line perpendicular to the given parallel lines and passes through (-5,4).
Any line perpendicular to the given lines is
x-y+k=0
This line passes through (-5,4). Therefore,
-5-4+k = 0
or k=9
Hence, the required line is
x-y+9=0