Question 1090943: A plot of land is in the shapf parallelogram 20m × 14m, the angle between the sides being 60 degree. Inscribe an elliptical bed on it. Use a suitable scale
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
A plot of land is in the  shape of parallelogram 20m × 14m, the angle between the sides being 60 degree.
Inscribe an elliptical bed on it. Use a suitable scale
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This problem is, obviously, above the standard school level.
Therefore, I will assume that your level corresponds to the level of the problem.
In accordance with this assumption, I will give you the idea only, leaving its implementation on you.
Place the parallelogram on the coordinate plane in a way
1) tts center (intersection point of its diagonals) is at the origin of the coordinate system;
2) the side of 20 m long is parallel to x- axis;
3) one of the two slant sides is the straight line y =  (1)
which has x-intercept (10,0) at x = 10.
I will take vertical semi-axis of the ellipse of b =  meters long. So the ellipse will touch the horizontal sides of 20 m long.
The length "a" of the horizontal semi-axis is unknown now.
The equation of the ellipse is
 +  = 1 (2)
with the unknown "a".
And you need to determine the length of the horizontal semi-axis "a" from the condition that the ellipse (2) and the straight line (1)
have only one common point.
In other words, you need to determine the length of the horizontal semi-axis "a" from the condition that the system of equations (1) and (2)
has only one solution.
Your task is two-fold.
First you need to understand that my construction is not self-contradictory; is feasible and makes sense.
Second, you need to find the unknown parameter "a" as described in the text above.
Good luck !!
And happy learning !!
I like when students come with interesting difficult problems.
If you have questions, send them to me in the THANK-YOU note.
In this case do not forget to mention the ID code of this problem, which is 1090943.
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