A tangent is drawn at any fixed point \( P \) on the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{9}...

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A tangent is drawn at any fixed point \( P \) on the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 \) and if chord of contact of the ellipse \( \frac{x^{2}}{9}+\frac{y^{2}}{16}=1 \) with respect to any point on this tangent passes through a fixed point, then prove that the line joining this fixed point to the point \( P \) never subtends right angle at the origin.
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