question_answer

If the point of intersection of the \[\frac{{{x}^{2}}}{{{a}^{2}}}\,+\,\frac{{{y}^{2}}}{{{b}^{2}}}\,=\,1\] and \[\frac{{{x}^{2}}}{{{\alpha }^{2}}}+\frac{{{y}^{2}}}{{{\beta }^{2}}}=1\] are at the extremities of the conjugate diameters of the former, then ______.     

A)  \[\frac{{{a}^{2}}}{{{\alpha }^{2}}}+\frac{{{b}^{2}}}{{{\beta }^{2}}}=2\]                     

B)  \[\frac{{{\alpha }^{2}}}{{{a}^{2}}}-\frac{{{\beta }^{2}}}{{{b}^{2}}}=2\]

C)  \[\frac{{{a}^{2}}}{{{\alpha }^{2}}}-\frac{{{b}^{2}}}{{{\beta }^{2}}}=2\]                       

D)  All the above

E)  None of these