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.

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- November 25th 2010, 07:17 AMRaeQuestions 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 - November 26th 2010, 06:44 AMOpalg
Take the origin to be at the base of the wall. When the ladder makes an angle with the wall, the coordinates (x,y) of the point 2 feet from the top of the ladder are . (Draw a diagram to make sure that you understand why that is.) Thus and . Now use the fact that to get an equation connecting x and y.

- November 28th 2010, 02:10 PMRae
Could you explain how you get (x,y) = (2sin theta, 6cos theta) ?

- November 29th 2010, 12:26 AMOpalg
- December 2nd 2010, 04:15 PMRae
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.