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Points P and D are taken on the ellipse ...

Points P and D are taken on the ellipse `(x^(2))/(4)+(y^(2))/(2)=1` . If a , b ,c and d are the lengths of the side of quadrilateral PADB, where A and B are foci of the ellipse, then maximum value of (abcd) is __________

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To solve the problem, we need to find the maximum value of the product of the lengths of the sides of the quadrilateral PADB, where P and D are points on the ellipse defined by the equation \(\frac{x^2}{4} + \frac{y^2}{2} = 1\), and A and B are the foci of the ellipse. ### Step-by-Step Solution: 1. **Identify the Ellipse Parameters:** The given equation of the ellipse is \(\frac{x^2}{4} + \frac{y^2}{2} = 1\). - Here, \(a^2 = 4\) and \(b^2 = 2\). - Thus, \(a = 2\) and \(b = \sqrt{2}\). ...
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