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  4. Equation of common tangent to ellipse 5 x2+2 y2=10, and hyperbola 11 x2-3 y2=33 is

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Q. Equation of common tangent to ellipse $5 x^2+2 y^2=10$, and hyperbola $11 x^2-3 y^2=33$ is

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Solution:

$c^2=a^2 m^2+b^2=a^2 m-b^2$
$2 m^2+5=3 m^2-11$
$\Rightarrow m^2=16=3 x^2-11 \Rightarrow y=\pm 4 x \pm 37$