A gardener marks an elliptical flower bed that is 10 metres long and 6 metres wide…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A gardener marks an elliptical flower bed that is metres long and metres wide. She pushes two pegs into the ground on the long axis, at the foci, and uses a loop of string. Find three things. First, the distance between the pegs. Second, the sum of the two straight parts of the string when the pencil is at any point of the bed. Third, the eccentricity of the bed.
Need a reminder? The key ideaShow
An ellipse has , , foci , directrices , latus rectum , and .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The semi-axes. metres and metres.
Step 2. The pegs. metres, so the pegs are metres apart.
Step 3. The string. For every point of the ellipse, metres.
Step 4. The eccentricity. .
Answer: the pegs are metres apart, the two parts of the string always add up to metres and . The whole loop is metres long.
Discussion (0)
Log in to join the discussion.
Loading…