The normal at one extrimity of latus rectum (in 1st quadrant) of the ellipse \( \frac{x^{2}}{a^{...

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The normal at one extrimity of latus rectum (in 1st quadrant) of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 ; ab0 \) meet the rectengular hyperbola \( x y=9 \) at point \( P \) and \( Q \) then
(a) If \( P \) is \( \left(6, \frac{3}{2}\right) \Rightarrow Q \) is \( \left(\frac{-3 \sqrt{2}}{2},-3 \sqrt{2}\right) \)
(b) Eccentricity of hyperbola is \( \sqrt{2} \)
(c) If \( P \) is \( \left(6, \frac{3}{2}\right) \Rightarrow Q \) is \( \left(-\frac{3 e}{2},-\frac{6}{e}\right) \) where \( e \) is eccentricity of the given ellipse
(d) If \( O \) is origin, then product of slopes of \( O P \) and \( O Q \) is positive
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