Find an ellipse centered through the origin that runs through 3 points

1. Apr 11, 2013

mahrap

Find the ellipse centered at the origin that runs through
the points (1,2), (2,2), and (3, I). Write your equation
in the form $$ax^2 + bxy + cy^2 = 1$$

I understand the $$ax^2$$ and $$cy^2$$ in the equation because the equation of an ellipse centered at origin is $$(x/a)^2 + (y/b)^2 = 1$$ so we let $$a = (1/a)^2$$ and $$b = (1/b)^2$$. but where did the $$bxy$$ come from?

2. Apr 11, 2013

Dick

$(x/a)^2 + (y/b)^2 = 1$ is only the equation of an ellipse centered at the origin whose axes are parallel to x and y axes. $ax^2 + bxy + cy^2 = 1$ is more general. It may be at an angle. Just put the given values for x and y in and get three equations to solve for the three unknowns a, b and c.