`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 the parabola y^(2)=8(x-3) to its directrix and S is an equilateral triangle, the length of side of the triangle is

If Q is the foot of the perpendicular from a point P on the parabola y = 8(x-3) to its directrix. S is the focus of the parabola and if SPQ is an equilateral triangle then the length of the side of the triangle is

The length of the perpendicular from the focus s of the parabola y^(2)=4ax on the tangent at P 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 sires of the parateral triangle SMP(where S is the focus of the parabola),is

The tangent at P to a parabola y^(2)=4ax meets the directrix at U and the latus rectum at V then SUV( where S is the focus)

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

A point on a parabola y^(2)=4ax, 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

the tangent drawn at any point P to the parabola y^(2)=4ax meets the directrix at the point K. Then the angle which KP subtends at the focus is

ABC is an equilateral triangle with A(0,0) and B(a,0),(a>0). L,M and N are the foot of the perpendiculars drawn from a point P to the side AB,BC, and CA, respectively.If P lies inside the triangle and satisfies the condition PL^(2)=PM.PN, then find the locus of P.