The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}x - 12a$$ is

From a point (d, 0) three normal are drawn to the parabola y² = x, then

The length of the chord of the parabola y² = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\alpha $$ with the axis of the parabola is

The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. Then, the length of the latusrectum is