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) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]
Correct Answer: C
Solution :
Given ellipse is \[\frac{{{x}^{2}}}{6}+\frac{{{y}^{2}}}{2}=1\] ?.(1) The equation of any tangent to it is \[y=2x\pm \sqrt{6{{m}^{2}}+2}\] ?(2) Also perpendicular to (2) through the center of ellipse is\[y=-\frac{1}{m}x\] ?(3) eliminating ?m? from (2) and (3) Gives the required locus as \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]
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