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 t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

If the normals at P(t_(1))andQ(t_(2)) on the parabola meet on the same parabola, then

Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .

The tangent and normal at P(t) , for all real positive t , to the parabola y^2= 4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, T and G is

Statement 1: The line a x+b y+c=0 is a normal to the parabola y^2=4a xdot Then the equation of the tangent at the foot of this normal is y=(b/a)x+((a^2)/b)dot Statement 2: The equation of normal at any point P(a t^2,2a t) to the parabola y^2 = 4ax is y=-t x+2a t+a t^3

If normal to parabola y^(2)=4ax at point P(at^(2),2at) intersects the parabola again at Q, such that sum of ordinates of the points P and Q is 3, then find the length of latus ectum in terms of t.

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

Find the equation of the tangent at t =2 to the parabola y^(2) = 8x .

Find the point where the line x+y=6 is a normal to the parabola y^2=8xdot