The equation of tangent to the curve $x^{2/3}+y^{2/3}=a^{2/3}$ at $(a,0)$ passes through which of the following points?

Differentiating the curve $x^{2/3}+y^{2/3}=a^{2/3}$ with respect to $x$:
$$\frac{2}{3}{x}^{-1/3}+\frac{2}{3}{y}^{-1/3}\frac{dy}{dx}=0$$
$$\frac{dy}{dx}=-\frac{x^{-1/3}}{y^{-1/3}}=-{\left(\frac{y}{x}\right)}^{1/3}$$
At the point $(a,0)$:
$$m={\frac{dy}{dx}|}_{(a,0)}=-{\left(\frac{0}{a}\right)}^{1/3}=0$$
The equation of the tangent at $(x_1,y_1)$ is $(y-y_1)=m(x-x_1)$.
$$(y-0)=0(x-a)⟹y=0$$
The equation of the tangent is $y=0$ (the x-axis).Among the given options, only $(2,0)$ lies on the x-axis.