An equilateral triangle is inscribed in the parabola `y^(2) = 4ax`, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

An equilateral triangle SAB in inscribed in the parabola y^2 = 4ax having it's focus at S. If chord lies towards the left of S, then the side length of this triangle is

Each side of an equilateral triangle subtends an angle of 60^(@) at the top of a tower h m high located at the centre of the triangle. If a is the length of each side of the triangle, then

The area of an equilateral triangle ABC is 17320.5 cm^(2) . With each vertex of the triangle as centre, a circle is drawn with radius to half the length of the side of the triangle (see the given figure). Find the area of the shaded region. (Use pi = 3.14 and sqrt(3) = 1.73205 )

If the equation of the base of an equilateral triangle is x+y=2 and the vertex is (2,-1) , then find the length of the side of the triangle.

The vertex of the parabola y^2+6x-2y+13=0 is

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

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.

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex if its slope is

If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpendicular drawn from the point P on the directrix of the parabola, then length of each sides of an equilateral triangle SMP(where S is the focus of the parabola), is