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8x^2+64xy+8y^2+12x+12y+9=0

I know Ax^2+Bxy+Cy^2+Dx+Ey+F=0

however, the professor is looking for an equation not an answer.

Here are my choices and I am stumped:

40x^2 + 12 sq rt2 x + 12 sq rt 2 y + 9 = 0

40x^2 - 24y^2 +12 sq rt2y +9 = 0

-24y^2 + 12 sq rt2x + 12 sq rt 2y + 9 = 0

40x^2 - 24y^ + 12 sq rt2x + 9 = 0

I am not sure what the process is to get to this point. I can run the basic Rotation Theorem for Conics and answer the problem with an angle degree.

PLEASE HELP!