The ellipse x^2+4 y^2=4 is inscribed in a rectangle aligned

Question:

The ellipse $x^{2}+4 y^{2}=4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point $(4,0)$. Then the equation of the ellipse is :-

  1. $4 x^{2}+48 y^{2}=48$

  2. $4 x^{2}+64 y^{2}=48$

  3. $x^{2}+16 y^{2}=16$

  4. $x^{2}+12 y^{2}=16$

Correct Option: , 4

Solution:

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