I really suck at proofs and I have this due tomorrow...any help would be appreciated. It doesn't count toward any points but I need to turn it in for credit

Definition: (1.3) Conics in $\displaystyle \mathbb{R}^2$. A conic in $\displaystyle \mathbb{R}^2$ is a plane curve given by the quadratic equation $\displaystyle q(x,y) = ax^2 + bxy +cy^2 + dx +ey +f = 0$

Here is my question:

Prove the statement in (1.3) that an affine transformation can be used to put any conic of $\displaystyle \mathbb{R}^2$ into one of the standard forms (a-1). (Hint: use a linear transformation $\displaystyle x \to Ax$ to take the leading term $\displaystyle ax^2 + by + cy^2$ into one of $\displaystyle \underline{+}x^2\underline{+}y^2$ or $\displaystyle \underline{+}x^2$ or $\displaystyle 0$; then complete the square in $\displaystyle x$ and $\displaystyle y$ to get rid of as much of the linear part as possible.

Thank you for your time and consideration. I will be up for awhile tonight to answer any questions and try to figure this out!