A vertical line passing through the point \( (h, 0) \) intersects the ellipse \( \frac{x^{2}}{4}...

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A vertical line passing through the point \( (h, 0) \) intersects the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{3}=1 \) at the points \( P \) and \( Q \). If the tangents to the ellipse at \( P \) and \( Q \) meet at the point \( R \) If \( \Delta(h)= \) area of the \( \Delta P Q R, \Delta_{1}=\max _{1 / 2 \leq h \leq 1} \Delta(h) \) and \( \Delta_{2}=\min _{1 / 2 \leq h \leq 1} \Delta(h) \), then \( \frac{8}{\sqrt{5}} \Delta_{1}-8 \Delta_{2} \) is equal to [Integer Type Question, 2013 Adv.]
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