`PC` is the normal at P to the parabola `y^2=4ax, C` being on the axis. `CP` is produced outwards to disothat `PQ =CP` ; show that the locus of Q is a parabola.

PG is the normal to a standard ellipse at P, G being on the major axis. GP is produced outwards to Q so that PQ = GP. Show that the locus of Q is an ellipse whose eccentricity is (a^2-b^2)/(a^2 +b^2) .

PQ is a double ordinate of the parabola y^2 = 4ax. If the normal at P intersect the line passing through Q and parallel to axis of x at G, then locus of G is a parabola with -

Normal at a point P on the parabola y^(2)=4ax meets the axis at Q such that the distacne of Q from the focus of the parabola is 10a. The coordinates of P are :

The normal at a point P on the parabola y^^2= 4ax meets the X axis in G.Show that P and G are equidistant from focus.

A normal drawn at a point P on the parabola y^(2)=4ax meets the curve again at O. The least distance of Q from the axis of the parabola,is

Find the locus of midpoint normal chord of the parabola y^(2)=4ax

PQ is normal chord of the parabola y^(2)=4ax at P(at^(2),2at) .Then the axis of the parabola divides bar(PQ) in the ratio