Equilateral traingles are circumscribed to the parabola `y^2=4ax` . Prove that their angular points lie on the conic `(3x+a)(x+3a)=y^2`

The length of the side of an equilateral triangle inscribed in the parabola,y^(2)=4x so that one of its angular point is at the vertex is:

An equilateral triangle is inscribed in the parabola y^(2)=4ax whose vertex is at of the parabola.Find the length of its side.

An equilateral triangle is inscribed in the parabola y^(2)=4ax where are at the vertex of the parabola.find the length of the side of the triangle.

y= -2x+12a is a normal to the parabola y^(2)=4ax at the point whose distance from the directrix of the parabola is

The angle between tangents to the parabola y^(2)=4ax at the points where it intersects with teine x-y-a=0 is (a>0)