I get a= 3/4, not 3/2!

I wondered about that myself. Geometrically, if draw a line from the origin to the point to the origin and look at the line symmetric to your line through that you should get another line satisfying the same properties. And, in fact there is another line!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?

BUT that other line cannot be written in the form y= ax+ b. What is the one line through (1, 2) that cannot be written y= ax+ b? Do you see that its distance to the origin is also 1, trivially?

I think you stuck in that "edit" while I was typing! Yes, that other line is x= 1.