`y=2x+c, 'c'` being variable is a chord of the parabola `y^2=4x`, meeting the parabola at A and B. Locus of a point dividing the segment AB internally in the ratio 1 : 1 is

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

The normals at the extremities of a chord PQ of the parabola y^2 = 4ax meet on the parabola, then locus of the middle point of PQ is

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments OQ internally in the ratio 1 : 3 , then the locus of P is _

Let O be the vertex and Q be any point on the parabola ,x^(2) =8y . If the point P divides the line segment OQ internally in the ratio 1: 3 then the locus of P is:

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.

Let O be the vertex and Q be any point on the parabola, x^2=""8y . It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :