Transform the equation $x^2 -2xy +y^2+x-3y$ to the axes through the point $(-1,0)$ parallel to the lines bisecting the angles between original axes.

Question

I have tried different methods of solving the problem but every time I seem to get different results. So, please help.

Q. Transform the equation $x^2 -2xy + y^2 + x -3y$ to the axes through the point $(-1,0)$ parallel to the lines bisecting the angles between original axes.![Is this correct? This was my try.] (https://i.stack.imgur.com/E5x6S.jpg)

Answer 1

Your approach is correct as proven by this desmos graph