question_answer

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

A)  \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]

B)  \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]

C)  \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]

D)  \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]

E)  None of these