Hint : for the given curve \(x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}, a > 0\)
Parametric Coordinates are \(x=a \cos ^3 \theta\)
\(y=a \sin ^3 \theta\)
\(\begin{gathered}
\frac{d y}{d x}=\text { slope of tangent at any }=\frac{d y / d \theta}{d x / d \theta} \\
\text { point }(x, y)
\end{gathered}\)
\(=\frac{3 a \sin ^2 \theta \cdot \cos \theta}{3 a \cos ^2 \theta(-\sin \theta)}=-\tan \theta\)
Equation of tangent at \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\)
\(y-a \sin ^3 \theta=-\tan \theta\left(x-a \cos^3 \theta\right)\)
its \(x\)-intercept \(=a \cos \theta\)
its \(y\)-intercept \(=a \sin \theta\)
So, the tangent cuts the axes at \(A(a \cos \theta, 0)\) and \(B(0, a \sin \theta)\) respectively.
\(A B=\sqrt{(a \cos \theta)^2+(a \sin \theta)^2}=a\), which is constant