Show that locus of vertices of the family of parabolas `y=(a^(3)x^(2))/(3)+(a^(2)x)/(2)-2a ` is xy=(105)/(64)`

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

The equation of the axis of the parabola (y+3)^(2)=4 (x-2) is

The vertex of the parabola y^(2)+4x-2y+3=0 is

The latusrectum of the parabola 13[(x-3)^(2)+(y-4)^(2) ]= (2x-3y+5)^(2)

The area included between the parabola y=(x^(2))/(4a) and the curve y=(8a^(3))/((x^(2)+4a^(2))) is

Solve (x^(3)-3xy^(2))dx+(3x^(2)y-y^(3))dy=0

Show that the locus of point of intersection of normals at the ends of a focal chord of the parabola y^(2) = 4ax is y^(2)= a(x- 3a).

Prove that the locus of point of intersection of two perpendicular normals to the parabola y^(2) = 4ax isl the parabola y^(2) = a(x-3a)