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\problemgrouptitle{Parallel, Perpendicular, and Normal Lines}

\item Find the line through the point $P(2,1)$ that is parallel to the tangent to the curve \mbox{$y=3x^2+2x+1$} at the point $Q(1,6)$\,.
\answer{Point-slope form: $y=8(x-2)+1$ , Slope-intercept form: $y=8x-15$}

\item Find the normal line to the curve $y=\sqrt{x}+x^2$ at the point $P(1,2)$\,.
\answer{Point-slope form: $\displaystyle y=-\frac{2}{5}(x-1)+2$ , Slope-intercept form: $\displaystyle y=-\frac{2}{5}x+\frac{12}{5}$}

\item Find any points on the curve $y=x^3-4$ with normal line having slope~$\displaystyle-\frac{1}{12}$\,.
\answer{$(-2,-12)$, $(2,4)$}
