I have no idea of what you are trying to say... :(

What do you mean by 'a'?

What do you need to do? Prove this? :confused:

Do you mean this:

xdx+ydy=\frac{a^{2}(xdx-ydy)}{x^{2}+y^{2}}

Because you have this written:

xdx+ydy=\frac{a^{2}(xdx-ydy)}{x^{2}}+y^{2}