question_answer

The locus of chords of contact of perpendicular tangents to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] touch another fixed ellipse is _______.

A)  \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=\frac{1}{{{a}^{2}}+{{b}^{2}}}\]         

B)  \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=\frac{2}{{{a}^{2}}-{{b}^{2}}}\]

C)  \[\frac{{{x}^{2}}}{{{a}^{4}}}+\frac{{{y}^{2}}}{{{b}^{4}}}=\frac{1}{{{a}^{2}}+{{b}^{2}}}\]         

D)  \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=\frac{2}{{{a}^{2}}+{{b}^{2}}}\]

E)  None of these