The queation is :
Show that the sum of the squares of the intersecting axes of the tangent plane at any point ($x_0$, $y_0$, $z_0$) of the surface $x^{2/3}$ +$y^{2/3}$ + $z^{2/3}$ = $a^{2/3}$ is constant.
My attemp with two variables using parametric subsitiution: $x=a{cos}^{3}\theta$ , and $y=a{sin}^{3}\theta$
and then find the tangent $\frac{dy}{dx} = - \frac{sin\theta}{cos\theta}$. The tangent equation then yields a constant as shown in the attached picture.
However, I could not prove it for three varialbles,
Any idea,