If 4x4+9y4=64 then the maximum value of x2+y2 is (where x and y are real)

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If $4 x^{4} + 9 y^{4} = 64$ then the maximum value of $x^{2} + y^{2}$ is (where x and y are real)

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$\frac{4}{\sqrt{3}}$

$\frac{4}{3} \sqrt{13}$

$\frac{32}{3}$

$\frac{32}{13}$

answer is B.

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Detailed Solution

Let $x^{2} = 4 \sin θ, y^{2} = \frac{8}{3} \cos θ \Rightarrow x^{2} + y^{2} = 4 \sin θ + \frac{8}{3} \cos θ$
$∴$ maximum value $= \sqrt{16 + \frac{64}{9}} = \frac{4 \sqrt{13}}{3}$

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