A tangent is drawn to the ellipse to cut the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and to cut the ellipse $\frac{x^2}{c^2}+\frac{y^2}{d^2}=1$ at the points P and Q. If the tangents are at right angles, then the value of $\left(\frac{a^2}{c^2}\right)+\left(\frac{b^2}{d^2}\right)$ is

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