# Thread: Questions on conic sections

1. ## Questions on conic sections

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

2. Originally Posted by Rae
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.
Take the origin to be at the base of the wall. When the ladder makes an angle $\theta$ with the wall, the coordinates (x,y) of the point 2 feet from the top of the ladder are $(x,y) = (2\sin\theta, 6\cos\theta)$. (Draw a diagram to make sure that you understand why that is.) Thus $\sin\theta = \frac12x$ and $\cos\theta = \frac16y$. Now use the fact that $\sin^2\theta + \cos^2\theta = 1$ to get an equation connecting x and y.

3. Could you explain how you get (x,y) = (2sin theta, 6cos theta) ?

4. Originally Posted by Rae
Could you explain how you get (x,y) = (2sin theta, 6cos theta) ?
Did you draw a diagram, as I suggested???

$\setlength{\unitlength}{2mm}
\begin{picture}(40,40)
\put(5.5,23.5){\bullet}
\put(0.5,28){ \theta}
\put(4.5,26.5){2}
\put(15,13){ 6}
\put(7,24){(x,y)}
\put(6,0){\line(0,1){24}}
\put(0,24){\line(1,0){6}}
\thicklines
\put(0,0){\line(0,1){40}}
\put(0,0){\line(1,0){40}}
\put(24,0){\line(-3,4){24}}
\end{picture}$

5. I did draw a diagram, but I guess I was thinking about the problem wrong because I didn't see it that way. Thanks for your help.