S.O.S. Mathematics CyberBoard

[mun]

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 be at a distance of 3 units from this point.

my work
i solved this and got the answer a line parallel to x axis .
first i find the equation of required line by taking its slope as m .i e [y-2=m(x+1)]. then i found the point of intersection of y-2=m(x+1) with the line x + y = 4 . after applying distance formula i got the answer as m=0 i.e a line parallel to x axis which is correct if we do calculation wise . but there is another answer which is a line parallel to y axis and i have checked this answer is geometrically correct.why analytically second answer is not coming.where is the fallacy.
_________________
There is no god in this world except PARENTS and i have lost ONE

[robbwrr]

Let (t,4-t) be the point on line x+y=4 then

produces two solutions etc.
_________________
"Those things that hurt, instruct."
-- Ben Franklin

[mun]

[Shadow]

[outermeasure]