PRQ is a variable chord of `y^2=4ax` and R is a point on the axis of the parabola such that `1/(PR^2)+1/(QR^2)` is independent of slope `barPO` then the point R is

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

The locus of the middle points of the focal chord of the parabola y^(2)=4ax , is

The locus of middle points of normal chords of the parabola y^(2) = 4ax is

If the normals drawn at the end points of a variable chord PQ of the parabola y^2 = 4ax intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points P and Q is

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

The slopes of the normal to the parabola y^(2)=4ax intersecting at a point on the axis of the parabola at a distance 4a from its vertex are in