Fixes for the hyperbola intuition exercise #161553

wrwrwr · 2015-11-25T19:05:32Z

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 · 2015-11-25T19:59:19Z

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.

wrwrwr added 5 commits November 25, 2015 17:32

Make the final equation describe a hyperbola with the correct center.

f92a15b

Rename variables to make the east-west hyperbola code more readable.

a50be01

Wiki calls the center (h, k). Let's stick to this.

Change hyperbola_intuition title to match its content.

f27ec26

Also reorder x_1 and y_1 to match answer fields in the east-west case.

Fix the equation in the intro to the south-north hyperbola case.

ed27ed5

Compare with the final hint. This is sometimes written with a -1 instead of a 1.

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Fixes for the hyperbola intuition exercise #161553

Fixes for the hyperbola intuition exercise #161553

wrwrwr commented Nov 25, 2015

wrwrwr commented Nov 25, 2015

Fixes for the hyperbola intuition exercise #161553

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Fixes for the hyperbola intuition exercise #161553

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wrwrwr commented Nov 25, 2015

wrwrwr commented Nov 25, 2015