Given system of equations are \( \Large \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}-\frac{zc}{c^{2}} = 1, \) \( \Large \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}} = 1 \) and \( \Large -\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}} = 1 \) On adding all these equations, we get,
\( \Large \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}} = 3 \)
\( \Large \frac{2z^{2}}{c^{2}}=2,\ \frac{2y^{2}}{b^{2}}=2,\ \frac{ax^{2}}{a^{2}} = 2 \) On subtracting (i) from (iv), (ii) equation from (iv) and (iii) from (iv) we get => \( \Large z = \pm \ c,\ y = \pm \ b,\ x = \pm \ a \)
