The equation $2x^{2}+xy+2y^{2} = 50$ represents an ellipse which lies obliquely in the plane; that is, an ellipse whose axes are not parallel to the coordinate axes. Find the slopes of the tangent lines to this ellipse at its $y$-intercepts. (Note: The slopes should be the same!)

The tangent lines to the ellipse at its $y$-intercepts have slope .