Hyperbola something wrong for me
Hello,
I'm French so please forgive my approximate English :).
I work on hyperbola. but I have an issue.
In the intro video Sal explain that hyperbolas can take two forms : horizontal (x²/a²)-(y²/b²)=1 & vertical (y²/b²)-(x²/a²)=1.
and give us this :
in green an ellipse, in purple horizontal hyperbola, in orange vertical hyperbola (pretty beautiful right ?!, we guess asymptote and the ellipse fit perfectly)
but in exercises : "Equation of a hyperbola from features"
I got wrong on a vertical hyperbola because "computer" want to me an equation of hyperbola like this : (y²/a²)-(x²/b²)=1
give us this :
in orange dotted line equation of a hyperbola as I learn in the videos. in orange full filled line equation of an hyperbola like asked in exercises.
from what I understand this a 90° rotation around the origin of the parabola ...
but how to known which form to use ? I'm lost
thanks :)
best regards
When the 1 is positive, the hyperbola is horizontal, and when it's negative, it's vertical.
If you were to permutate "a" and "b", then the conic would change a lot, but not in a 90° rotation. In general, I always consider "a" to correspond to the component of the mesh along the x-axis, and "b" to be along the y-axis (this applies to both horizontal and vertical hyperbolas, as well as ellipses, and by definition circles too).
To achieve a 90° rotation of the graph, you would have to permutate "x" and "y" from the equation of the hyperbola. Just like reciproqual functions, this will flip the graph along the 45° line of y=x.
Hope this helps!
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