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

Question

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

$xy = {{105} \over {64}}$

$xy = {{3} \over {4}}$

$xy = {{35} \over {16}}$

$xy = {{64} \over {105}}$

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