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 find length of each sides of an equilateral triangle SMP(where S is the focus of the parabola).

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

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

Foot of the directrix of the parabola y^(2) = 4ax is the point

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

If Q is the foot of the perpendicular from a point p on the parabola y^(2)=8(x-3) to its directrix. S is an equilateral triangle then find the lengh of side of the triangle.

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

Let x+y=k be a normal to the parabola y^(2)=12x . If p is the length of the perpendicular from the focus of the parabola onto this normal then 4k-2 p^(2) =?

The locus of foot of the perpendiculars drawn from the focus on a variable tangent to the parabola y^2 = 4ax 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

A point P on the parabola y^2=12x . A foot of perpendicular from point P is drawn to the axis of parabola is point N. A line passing through mid-point of PN is drawn parallel to the axis interescts the parabola at point Q. The y intercept of the line NQ is 4. Then-