Problem to prove that the given f(z)is analytic at the radius of the curve and Non Analytic at y=ax3

JNTU B.Tech M4 Maths. Chapter- Function of Complex Variable. Test on Analyticity of given function f(z) defined as f(z)=x^3y(y-ix)/x^6+y^2 at z not equal to zero, f(z)=0 at z=0.