The locus of the vertices of the family of parabolas $y = \frac{a^3 x^2}{3} + \frac{a^2x}{2} - 2a$ is :

Question

( A ) $xy = \frac{64}{105}$
( B ) $xy = \frac{3}{4}$
( C ) $xy = \frac{35}{16}$
( D ) $xy = \frac{105}{64}$