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

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.

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

Prove that the point on the parabola y^(2) = 4ax (a gt0) nearest to the focus is its vertex.

Prove that the point on the parabola y^(2) = 4ax (a gt0) nearest to the focus is its vertex.