Slope of the normal to the curve _$x=t^2+3t-8$ , _{$y=2t^2-2t-5$} , at the point P(2, -1) is given by

_$x=t^2+3t-8$ ,  _{$y=2t^2-2t-5$}  at (2, -1)

_$t^2+3t-8=2$  and _{$2t^2-2t-5=-1$}

_{$\Rightarrow t^2+3t-10=0$}  and _{$2t^2-2t-4=0$}

_{$\Rightarrow (t-2)t+5)=0$} and _{$(t+1)(t-2)=0$}

_{$\Rightarrow t=-5or2$   $\Rightarrow t=-1;t=2$}

_{$\Rightarrow t=2$}

_$\therefore$  slope of normal = _{$-\frac{7}{6}$}