[TEX]\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 0 [/TEX]
[TEX]\Rightarrow \frac{xbc + yac + zab}{xyz} = 0[/TEX]
[TEX]\Rightarrow xbc + yac + zab = 0[/TEX]
[TEX]\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 2[/TEX]
[TEX]\Rightarrow \frac{a^2}{x^2} + \frac{b^2}{y^2} + \frac{c^2}{z^2} + 2 .(\frac{ab}{xy} + \frac{bc}{yz} + \frac{ac}{zx}) = 4 [/TEX]
[TEX]\Rightarrow \frac{a^2}{x^2} + \frac{b^2}{y^2} + \frac{c^2}{z^2} + 2 .(\frac{abz +bcx+ acy}{xyz}) = 4[/TEX]
[TEX]\Rightarrow \frac{a^2}{x^2} + \frac{b^2}{y^2} + \frac{c^2}{z^2} = 4[/TEX]