At any point P on the parabola `y^2 -2y-4x+5=0` a tangent is drawn which meets the directrix at Q. Find the locus of point R which divides QP externally in the ratio `1/2:1`

At any point P on the parabola y^2-2y-4x+5=0 , a tangent is drawn which meets the directrix at Q. Find the locus of R which divides P externally in the ratio 1/2:1 .

Let P be a point on the parabola y^(2) - 2y - 4x+5=0 , such that the tangent on the parabola at P intersects the directrix at point Q. Let R be the point that divides the line segment PQ externally in the ratio 1/2 : 1. Find the locus of R.

The ordinates of points P and Q on the parabola y^2 = 12x are in the ratio 1 : 2. Find the locus of the point of intersection of the normals to the parabola at P and Q.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

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

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x. These tangents meet the line x=2 at P and Q, then length of PQ is

If Q is a point on the locus of x^(2)+y^(2)+4x-3y+7=0 , then find the equation of locus of P which divides segment OQ externally in the ratio 3:4, where O is origin.