Question

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?

Answer 1

might help to complete some square

Answer 2

\[x^2 + 3xy + 2y^2 - 3x + 2y + 10 = 0\]
\[(x^2-3x) + (2y^2+2y) + 3xy+ 10 = 0\]
\[(x^2-3x+\frac94) + 2(y^2+y+\frac14) + 3xy+ 10-\frac94-\frac12 = 0\]
\[(x-\frac32)^2 + 2(y+\frac12)^2 + 3xy+\frac{29}4 = 0\]
\[(x-\frac32)^2 + 2(y+\frac12)^2= -3xy-7.25\]
i know theres a different approach to this, but i cant recall the details at the moment

Answer 3

@jungleman There Ya Go