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

Show that an equation of the normal to the parabola with equation $\displaystyle y^2=4ax $ at the point P$\displaystyle (at^2,2at)$ is $\displaystyle y+tx=2at+at^3$

This normal meets the parabola again at the point Q$\displaystyle (as^2, 2as)$

Show that s+t+$\displaystyle \frac{2}{t}$=0

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