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Question

# The equation of a straight line passing through the point (-5, 4) and which cuts off in intercept of √2 unit. between the lines x+y+1=0 and x+y−1=0 is:

A
2xy+14=0
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B
3x+y+11=0
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C
xy+9=0
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D
4x+5y=0
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Solution

## The correct option is C x−y+9=0Let the given point be A(x1,y1)=(−5,4) and the given lines be x+y+1=0......(1) x+y−1=0......(2) Observe that, From equation (1) to, Let AM is perpendicular distance Then, AM=|−5+4−1|√12+12=2√2=√2 Let B is any point on equation (2)to, From equation (2) x+y−1=0 y=−x+1 On comparing that, y=mx+c Then, m=−1 Slope of perpendicular line is m1=−1m=1 Then, equation of line is y−y1=m(x−x1) ⇒y−4=1(x+5) ⇒y−4=x+5 ⇒x−y+5+4=0 ⇒x−y+9=0 Hence, this is the answer.

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