If the tangent to the curve x^(3)+y^(3)=...

If the tangent to the curve `x^(3)+y^(3)=a^(3)` at the point `(x_(1),y_(1))` intersects the curve again at the point `(x_(2),y_(2))`, then show that, `(x_(2))/(x_(1))+(y_(2))/(y_(1))+1=0`.

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