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For complex number z, let Im(z) denote the imaginary part of z. Let S be the set of all complex number satisfying $5 z^{2} + 5 {\bar{z}}^{2} + 26 z \bar{z} = 144$ then maximum possible value of, $| z_{1} - z_{2} |, w h e r e z_{1}, z_{2} \in S, Im (z_{1}) > 0 a n d Im (z_{2}) < 0, i s_______$

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answer is B.

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Detailed Solution

$5 {(x + i y)}^{2} + 5 {(x - i y)}^{2} + 26 x^{2} + 26 y^{2} = 144 10 x^{2} - 10 y^{2} + 26 x^{2} + 26 y^{2} = 144 36 x^{2} + 16 y^{2} = 144 \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

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