MathematicsIf the ellipse x2a2+y2b2=1 is inscribed in a rectangle whose length to breadth ratio is 2 : 1 then the area of the rectangle is

If the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is inscribed in a rectangle whose length to breadth ratio is 2 : 1 then the area of the rectangle is

$\frac{L}{B} = \frac{2 a}{2 b} = \frac{2}{1} \Rightarrow a = 2 b Area of rectangle = L \times B = 2 a (2 b) = 2 a^{2} = \frac{8}{5} (a^{2} + b^{2})$

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