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

In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :

Angle between the tangents to the curve $$y = {x^2} - 5x + 6$$ at the points $$(2,0)$$ and $$(3,0)$$ is

The set of points where $$f\left( x \right) = {x \over {1 + \left| x \right|}}$$ is differentiable is