Prove that the normal at `(am^(2),2am)` to the parabola `y^(2)=4ax` meets the curve again at an angle `tan^(-1)((1)/(2)m)`.

Prove that the normals at the points (1,2) and (4,4) of the parbola y^(2)=4x intersect on the parabola.

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

If the normal at the point ( bt_(1)^(2), 2 bt_(1)) to the parabola y^(2)= 4bx meets it again at the point ( bt_(2)^(2), 2 bt_(2)) , then-

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

Length of the shortest normal chord of the parabola y^2=4ax is

Show that the normal to the rectangular hyperbola xy=c^(2) at point t meet the curve again at t' such that t^(3)t'=1 .

If the straight line lx + my=1 is a normal to the parabola y^(2)=4ax , then-

find equation of normal at point (am^2, am^3) to the curve ay^2=x^3

If a normal to a parabola y^2 =4ax makes an angle phi with its axis, then it will cut the curve again at an angle