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

. A conic in

is a plane curve given by the quadratic equation

Here is my question:

Prove the statement in (1.3) that an affine transformation can be used to put any conic of

into one of the standard forms (a-1). (Hint: use a linear transformation

to take the leading term

into one of

or

or

; then complete the square in

and

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!