`P, Q` are the points `\'t_1\', \'t_2\'` on the parabola `y^2 = 4ax`. If the normals at `P, Q` meet on the parabola at `R`, show that `T_1 t_2 = 2`. Also find the locus of the mid-point of `PQ`.

P(t_1) and Q(t_2) are the point t_1a n dt_2 on the parabola y^2=4a x . The normals at Pa n dQ meet on the parabola. Show that the middle point P Q lies on the parabola y^2=2a(x+2a)dot

P(t_1) and Q(t_2) are the point t_1a n dt_2 on the parabola y^2=4a x . The normals at Pa n dQ meet on the parabola. Show that the middle point P Q lies on the parabola y^2=2a(x+2a)dot

P(t_(1)) and Q(t_(2)) are the point t_(1) and t_(2) on the parabola y^(2)=4ax. The normals at P and Q meet on the parabola.Show that the middle point PQ lies on the parabola y^(2)=2a(x+2a)

If the normals at points ' t_(1) " and ' t_(2) ' to the parabola y^(2)=4 a x meet on the parabola, then

P(t_(1))andQ(t_(2)) are points t_(1)andt_(2) on the parabola y^(2)=4ax . The normals at P and Q meet on the parabola. Show that the middle point of PQ lies on the parabola y^(2)=2a(x+2a) .

P(t_(1))andQ(t_(2)) are points t_(1)andt_(2) on the parabola y^(2)=4ax . The normals at P and Q meet on the parabola. Show that the middle point of PQ lies on the parabola y^(2)=2a(x+2a) .

Normal at P(t1) cuts the parabola at Q(t2) then relation

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) .

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