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

Answer

`tan^(-1)|(t)/(2)|`

Explanation

Slope of normal at point P(t)=-t
or Slope of line PQ=-t
Now, point Q has parameter
`-t-(2)/(t)`
Slope of tangent at point `Q=(1)/(-t-(2)/(t))=(-t)/(t^(2)+2)`
Now, the angle between the normal and the parabola at Q is equivalent to the angle between the normal and the tangent at point Q. Therefore,
`tantheta=|(-t+(t)/(t^(2)+2))/(1+t(t)/(t^(2)+2))|=|(t)/(2)|`
Hence, `theta=tan^(-1)|(t)/(2)|`