If the equation of a hyperbola is
( x² / a² ) - ( y² / b² ) = 1,
then the joint of equation of its Asymptotes is
( x² / a² ) - ( y² / b² ) = 0.
Note that these two equations differ only
in the constant term.
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denominators
denominators
hyperbola
ellipse are added hyperbola are subtracted
Ellipse
denominators
denominators
An asymptote of a curve is a line where the distance of the curve and line approach zero as they tend to infinity (they get closer and closer without ever meeting) If one zooms out of a hyperbola, the straight lines are usually asymptotes as they get closer and closer to a specific point, yet do not reach that point.
hyperbola
hyperbola
ellipse are added hyperbola are subtracted
Hyperbolae with different eccentricities have a different angle between their asymptotes.
Ellipse
Inverse
A right hyperbola shape.
A formula is an equation that expresses a relationship between measurements.
Both the ellipse and the hyperbola has an x squared and a y squared term. In the ellipse, they are both positive. In the hyperbola, one of them is negative. Example: 3x^2 /36 + 5y^2 / 64 = 1 (ellipse) 3x^2 / 36 - 5y^2 / 64 = 1 (hyperbola)