## Normal of parabola cuts the curve again identity

A curve is given parametrically by $x=ct, y=\frac{c}{t}$. Show that an equation of the tangent to the curve at the point (ct, $\frac{c}{t}$) is $x+t^2y=2ct$(solved)

Show that an equation of the normal to the parabola with equation $y^2=4ax$ at the point P $(at^2,2at)$ is $y+tx=2at+at^3$
This normal meets the parabola again at the point Q $(as^2, 2as)$
Show that s+t+ $\frac{2}{t}$=0

Could not show it, Stuck at: $\frac{2}{t}\pm2a(t^2+1)$ Help