Thread: 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

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 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.

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

Originally Posted by Rae

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

Did you draw a diagram, as I suggested???

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.