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@wrwrwr wrwrwr commented Nov 25, 2015

A few fixes:

  • the title includes ellipse, but there are just two hyperbola problems in the file;
  • the equation in the intro to the south-north case has signs flipped;
  • the equation in the intro to the east-west case has axes swapped;
  • the final hint in the east-west case gives an ellipse with center coordinates and axes swapped;

plus some minor readability improvements.

Some references:

  • Wiki, lists equations for both cases;
  • Mathworld, derives the east-west case (equations 3-8);
  • EoM, another one with the same notation for axes.

One possibility for testing is to copy the equation from the final hint to Alpha. Clicking "Properties" gives foci, center etc.

The semi-major axis (a) is the distance from the center to a vertex
(horizontal distance in this case), and the semi-minor axis (b) is
the distance from a vertex to an asymptote along a tangent (vertical
in this case).
Wiki calls the center (h, k). Let's stick to this.
Also reorder x_1 and y_1 to match answer fields in the east-west case.
Compare with the final hint. This is sometimes written with a -1
instead of a 1.
@wrwrwr
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wrwrwr commented Nov 25, 2015

One more thing that could be improved is the 7th hint -- it shows how to calculate the semi-minor axis, but doesn't say what it is.

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