Rotated Quadratic Equations

A) Use the Discriminant test to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola.

B) Find a suitable rotation of axis

C) Find an equation for the graph in a - plane

D) Sketch the graph over top both coordinate systems with your angle of rotation displayed.

My Work:

A) So, The equation is a parabola.

B) Here's where I get somewhat confused, so bear with my work.

From here on I'm not really quite sure what to do. The notes I have on this don't really give me enough help to continue on. I know later on though I have to utilize these: