`y = sqrt(3)x +lambda` is drawn through focus S of the parabola `y^(2)= 8x +16`. If two intersection points of the given line and the parabola are A and B such that perpendicular bisector of AB intersects the x-axis at P then length of PS is

The equation of a line drawn through the focus of the parabola y^(2)=-4 x at an angle of 120^(circ) to the x-axis is

A focal chord for parabola y^(2)=8(x+2) is inclined at an angle of 60^(@) with positive x-axis and intersects the parabola at P and Q. Let perpendicular bisector of the chord PQ intersects the x-axis at R, then the distance of R from focus is :

A focal chord for parabola y^(2)=8(x+2) is inclined at an angle of 60^(@) with positive x-axis and intersects the parabola at P and Q. Let perpendicular bisector of the chord PQ intersects the x-axis at R, then the distance of R from focus is :

A line L passing through the focus of the parabola (y-2)^(2)=4(x+1) intersects the two distinct point. If m be the slope of the line I,, then

A line L passing through the focus of the parabola (y-2)^(2)=4(x+1) intersects the two distinct point. If m be the slope of the line I,, then

Consider the parabolas y^2=4x , x^2=4y Find the point of intersection of the two parabolas.

Find the points of intersection of the parabola y^2=8x and the line y=2x.

A tangent is drawn to the parabola y^(2)=8x at P(2, 4) to intersect the x-axis at Q, from which another tangent is drawn to the parabola to touch it at R. If the normal at R intersects the parabola again at S, then the coordinates of S are