The locus of the vertex of the family of parabolas
`y=(a^(3)x^(2))/(3)+(a^(2)x)/(2)-2a` is

The locus of the vertices of the family of parabolas y =[a^3x^2]/3 + [a^2x]/2 -2a is:

The vertex of the parabola y^2 + 4x = 0 is

Find the vertex of the parabola x^2=2(2x+y)

The vertex of the parabola y^2 = 4x + 4y is

The vertex of the parabola x^(2)=8y-1 is :

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

The locus of the center of a circle which cuts orthogonally the parabola y^2=4x at (1,2) is a curve

Find the vertex, focus and directrix of the parabola x^(2)=2(2x+y) .

If the area of the triangle whose one vertex is at the vertex of the parabola, y^(2) + 4 (x - a^(2)) = 0 and the other two vertices are the points of intersection of the parabola and Y-axis, is 250 sq units, then a value of 'a' is