Find the point on the parabola `y^2= 4ax (a > 0)` which forms a triangle of area `3a^2` with the vertex and focus of the parabola.

Find the point on the parabola y^(2)=4ax(a gt 0) which forms a triangle of area 3a^(2) with the vertex and focus of the parabola .

Find the locus of the middle points of the chords of the parabola y^(2)=4ax which subtend a right angle at the vertex of the parabola.

Find the vertex and focus of the given parabola x^(2)+4y=0

Find the coordinates of the vertex and the focus of the parabola y^(2)=4(x+y) .

An equilateral triangle is inscribed in the parabola y^(2)=4ax, such that one vertex of this triangle coincides with the vertex of the parabola.Then find the side length of this triangle.

Find the locus of the mid-points of the chords of the parabola y^(2)=4ax which subtend a right angle at vertex of the parabola.

Find the locus of the mid-points of the chords of the parabola y^2=4ax which subtend a right angle at vertex of the parabola.