`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.

PC is the normal at P to the parabola y^2=4ax, C being on the axis. CP is produced outwards to Q so that 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) .

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 normal at a point P to the parabola y^2=4ax meets axis at G. Q is another point on the parabola such that QG is perpendicular to the axis of the parabola. Prove that QG^2−PG^2= constant

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 :

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

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.