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;

Thus

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?