question_answer

Let a, b, c be positive real numbers. The following system of equations in x, y and z \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{z}^{2}}}{{{c}^{2}}}=1,\] \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}+\frac{{{z}^{2}}}{{{c}^{2}}}=1\] and \[\frac{-{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}+\frac{{{z}^{2}}}{{{c}^{2}}}=1,\] has

A)  no solution

B)  unique solution

C)  infinitely many solutions

D)  finitely many solutions

E)  None of these