question_answer

What is the locus of point of intersection of tangents of \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] drawn at the extremities of a chord subtending \[90{}^\circ \] at origin is         

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

B)  \[\frac{{{x}^{2}}}{{{a}^{4}}}+\frac{{{y}^{2}}}{{{b}^{4}}}={{\left( \frac{1}{{{a}^{{}}}}+\frac{1}{b} \right)}^{2}}\]

C)  \[{{a}^{2}}{{x}^{2}}+{{b}^{2}}{{y}^{2}}{{({{a}^{2}}+{{b}^{2}})}^{2}}\]

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