question_answer

If \[\frac{x}{a}\cos \alpha +\frac{y}{b}\sin \alpha =1,\] \[\frac{x}{a}\cos \beta +\frac{y}{b}\sin \beta =1\] and  \[\frac{\cos \alpha .\cos \beta }{{{a}^{2}}}+\frac{\sin \alpha .\sin \beta }{{{b}^{2}}}=0,\] then _______.

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

B)  \[\tan \alpha .\tan \beta =\frac{{{b}^{2}}({{x}^{2}}+{{a}^{2}})}{{{a}^{2}}({{y}^{2}}+{{b}^{2}})}\]

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

D)  All of the above

E)  None of these