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An ellipse \( x^{2}+4 y^{2}=4 \) 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
P same point of the ellipse in in its new position is given by the curve \( \left(x^{2}+y^{2}\right)^{2}=\lambda\left(x^{2}+y^{2}\right)+\mu x y \) where \( \lambda \) and \( \mu \) are positive integers.
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Find the value of \( (\lambda+\mu) \).
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