An ellipse `x^2+4y^2 =4` is rotated anticlockwise through a right angle in its own plane about its centre. If the locus of the point of intersection of a tangent to ellipse in its origin position with the tangent at the same point of the ellipse in its new position is given by the curve `(x^2+y^2)^2=lambda(x^2+y^2)+mu xy` where `lambda` and `mu` are positve integers. Find the value of `(lambda+mu)`