The locus of the foot of perpendicular drawn from the centre

Question:

The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2}+3 y^{2}=6$ on any tangent to it is :-

  1. $\left(x^{2}-y^{2}\right)^{2}=6 x^{2}+2 y^{2}$

  2. $\left(x^{2}-y^{2}\right)^{2}=6 x^{2}-2 y^{2}$

  3. $\left(x^{2}+y^{2}\right)^{2}=6 x^{2}+2 y^{2}$

  4. $\left(x^{2}+y^{2}\right)^{2}=6 x^{2}-2 y^{2}$


Correct Option: , 3

Solution:

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