Question

Graph the conic:

Answer 1

guess I would start by isolating \(y\) and find the horizontal/vertical asymptotes

Answer 2

We're suppose to rotate the coordinate the planes, I'm not sure how to do that..

Answer 3

*rotate the coordinate plane

Answer 4

So far I know it's a hyperbola by using the discriminant

Answer 5

yeah
angle of rotation for eliminating xy term :
\[\large \cot(2\theta) = \dfrac{A-C}{B}\]

http://math.sci.ccny.cuny.edu/document/show/2685

Answer 6

\[\large \cot (2\theta) = \dfrac{0-0}{1} = 0 \implies \theta = \dfrac{\pi}{4}\]

Answer 7

\(\large x = x'\cos \theta - y' \sin \theta\)
\(\large y = x'\sin \theta + y' \cos\theta\)

Answer 8

http://www.wolframalpha.com/input/?i=%28x%2Fsqrt%282%29-y%2Fsqrt%282%29%29%28x%2Fsqrt%282%29%2By%2Fsqrt%282%29%29+-+2%28x%2Fsqrt%282%29%2By%2Fsqrt%282%29%29+-+4%28x%2Fsqrt%282%29-y%2Fsqrt%282%29%29+%3D+0