The locus of the foot of perpendicular drawn from the centre

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

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

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

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