Solution to falling ladder problem
Problem
What's the equation of the curve consisting of all points lying 4 feet from the x-axis along a 12-foot line segment in the first quadrant whose endpoints are on the axes?
Answer
The equation is
the equation of an ellipse.
Justification
Let U be an arbitrary point on the curve, and let (x , y) be its coordinates. From the picture
we see that we have two similar right triangles, ACU and UDB . Similarity gives us
By the Pythagorean Theorem,
