A point on a parabola `y^2=4a x ,` the foot of the perpendicular from it upon the directrix, and the focus are the vertices of an equilateral triangle. The focal distance of the point is equal to `a/2` (b) `a` (c) `2a` (d) `4a`

A point P on the parabola y^(2)=4x , the foot of the perpendicular from it upon the directrix and the focus are the vertices of an equilateral triangle. If the area of the equilateral triangle is beta sq. units, then the value of beta^(2) is

If a point P on y^2x , the foot of the perpendicular from P on the directrix and the focus form an equilateral traingle , then the coordinates of P may be

Find the foot of the perpendicular from the point (2,4) upon x+y=1

M is the foot of the perpendicular from a point P on the parabola y^(2)=8(x-3) to its directrix and S is an equilateral triangle, the length of side of the triangle is

M is the foot of the perpendicular from a point P on a parabola y^(2)=4ax to its directrix and SPM is an equilateral triangle,where S is the focus.Then find SP.

Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3) , 5) are the vertices of an equilateral triangle.

Show that the points A(1,2),B(1,6), C(1 + 2sqrt(3),4) are the vertices of an equilateral triangle .

Prove that the points (2a, 4a), (2a, 6a) and (2a+ sqrt(3) a, 5a) are the vertices of an equilateral triangle.

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 sires of the parateral triangle SMP(where S is the focus of the parabola),is