1) Describe the curve traced out by a point 2 feet from the top of an 8-foot ladder as the bottom of the ladder moves away from a vertical wall.
Thank you
Take the origin to be at the base of the wall. When the ladder makes an angle $\displaystyle \theta$ with the wall, the coordinates (x,y) of the point 2 feet from the top of the ladder are $\displaystyle (x,y) = (2\sin\theta, 6\cos\theta)$. (Draw a diagram to make sure that you understand why that is.) Thus $\displaystyle \sin\theta = \frac12x$ and $\displaystyle \cos\theta = \frac16y$. Now use the fact that $\displaystyle \sin^2\theta + \cos^2\theta = 1$ to get an equation connecting x and y.
Did you draw a diagram, as I suggested???
$\displaystyle \setlength{\unitlength}{2mm}
\begin{picture}(40,40)
\put(5.5,23.5){$\bullet$}
\put(0.5,28){$ \theta$}
\put(4.5,26.5){$2$}
\put(15,13){$ 6$}
\put(7,24){$(x,y)$}
\put(6,0){\line(0,1){24}}
\put(0,24){\line(1,0){6}}
\thicklines
\put(0,0){\line(0,1){40}}
\put(0,0){\line(1,0){40}}
\put(24,0){\line(-3,4){24}}
\end{picture}$