Describe the graph of (2x + 3y)^2 - (x + y)^2 = 1 + 10xy. What kind of conic section is it?
(2x + 3y)2 - (x + y)2 = 1 + 10xy
(4x2 + 12xy + 9y2) - (x2 + 2xy + y2) = 1 + 10xy
4x2 + 12xy + 9y2 - x2 - 2xy - y2 = 1 + 10xy
3x2 + 10xy + 8y2 = 1 + 10xy
3x2 + 8y2 = 1
This is an ellipse -- center at (0,0) x-radius = 1/sqrt(3) y-radius = 1/sqrt(1/8)
