Cartesian equation equivalent to polar equation
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1. Rotate the coordinate axes x and y by the appropriate acute angle theta, so as to eliminate the cross product term (xy) from the equation x^2 + xy + y^2 - 6 = 0. State the value of theta, give the transformed equation in terms of the new rotated coordinates u and v, and identify the figure it represents.
2. Find cartesian equation that is equivalent to the following polar equation, then sketch and identify its graph.
r = 8/(sin theta - 2 cos theta)
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