identify the graph of the equation x^2 + 3xy + 2y^2 - 3x + 2y + 10 = 0, then find out the theta, and angle of rotation..*can yuu help me step by step how to do this and how to figure out what kind of graph this is?*

Question

anonymous · Answer

This is the equation a general quadratic, usually an ellipse or hyperbola.
You can complete the square, then translate to the origin to have an equation like
Ax^2+Bxy+Cy^2+F = 0
The inclination (rotation) theta (from standard position) in (-pi/2,pi/2) is 
theta = pi/4 if A=C else 1/2 arctan(B/(A-C))