Q. 164.0( 44 Votes )

Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

Answer :

Let y = mx + c be the line through points (-1, 2).


2 = m (-1) + c


c = m + 2


Thus, y = mx + m + 2 --------------- (1)


The given line as


x + y = 4 ------------ (2)


On solving these equations, we get,


and


Thus, is the point of intersection of lines (1) and (2).


Since, this point is at a distance of 3 units from point (-1, 2),


So, now using distance formula,






1 + m2 = m2 + 1 + 2m


2m = 0


m = 0


Therefore, the slope of the required line must be zero,


Hence, the line must be parallel to the x – axis.


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