Difference between revisions of "Hyperbola"
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A '''hyperbola''' is defined as the [[locus]] of [[point]]s such that the difference between the distances to the two [[focus|foci]] is constant. It is the [[conic section]] formed by slicing two cones such that the plane of the cut never intersects the center line of the cones. | A '''hyperbola''' is defined as the [[locus]] of [[point]]s such that the difference between the distances to the two [[focus|foci]] is constant. It is the [[conic section]] formed by slicing two cones such that the plane of the cut never intersects the center line of the cones. | ||
| − | <math>\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} = 1</math> is the standard form of a horizontally opening hyperbola, while <math>\frac{(y-k)^2}{b^2}-\frac{(x-h)^2}{a^2} = 1</math> is the standard form of a vertically opening one. Also, <math>xy=k</math> for some real number <math>k</math> is a hyperbola. | + | <math>\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} = 1</math> is the standard form of a horizontally opening hyperbola, while <math>\frac{(y-k)^2}{b^2}-\frac{(x-h)^2}{a^2} = 1</math> is the standard form of a vertically opening one. Also, the graph of <math>xy=k</math> for some real number <math>k</math> is a hyperbola. |
Revision as of 11:56, 31 March 2018
A hyperbola is defined as the locus of points such that the difference between the distances to the two foci is constant. It is the conic section formed by slicing two cones such that the plane of the cut never intersects the center line of the cones.
is the standard form of a horizontally opening hyperbola, while 
is the standard form of a vertically opening one. Also, the graph of 
for some real number 
is a hyperbola.
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