The question is;
Find the equations of the lines which pass through the point and have perpendicular distance of from the origin.
The question says "lines" and "equations". The plural makes me think I have gone wrong since I only have one. Here is working....
Let be a line which passes through then for some . Let the line perpendicular to passing through the origin be and thus .
Let and intersect at then;
Let the distance between and the origin be then,
and therefore the required line is
The question says lines though. Did I do something wrong? or wrong method?
Thank you in advance.
Edit: Since I defined a as a real number of some sort is it right that a might not be a real number and thus the other line is . Is this right?