{"id":2371,"date":"2016-11-03T20:43:33","date_gmt":"2016-11-03T20:43:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&p=2371"},"modified":"2017-04-04T19:57:32","modified_gmt":"2017-04-04T19:57:32","slug":"summary-the-hyperbola","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/summary-the-hyperbola\/","title":{"raw":"Summary: The Hyperbola","rendered":"Summary: The Hyperbola"},"content":{"raw":"
Key Equations<\/h2>\r\n
\r\n\r\n
\r\n
Hyperbola, center at origin, transverse axis on x<\/em>-axis<\/td>\r\n
A hyperbola is the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the difference of the distances between [latex]\\left(x,y\\right)[\/latex] and the foci is a positive constant.<\/li>\r\n \t
The standard form of a hyperbola can be used to locate its vertices and foci.<\/li>\r\n \t
When given the coordinates of the foci and vertices of a hyperbola, we can write the equation of the hyperbola in standard form.<\/li>\r\n \t
When given an equation for a hyperbola, we can identify its vertices, co-vertices, foci, asymptotes, and lengths and positions of the transverse and conjugate axes in order to graph the hyperbola.<\/li>\r\n \t
Real-world situations can be modeled using the standard equations of hyperbolas. For instance, given the dimensions of a natural draft cooling tower, we can find a hyperbolic equation that models its sides.<\/li>\r\n<\/ul>\r\n
Glossary<\/h2>\r\ncenter of a hyperbola<\/strong> the midpoint of both the transverse and conjugate axes of a hyperbola\r\n\r\nconjugate axis<\/strong> the axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints\r\n\r\nhyperbola<\/strong> the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the difference of the distances between [latex]\\left(x,y\\right)[\/latex] and the foci is a positive constant\r\n\r\ntransverse axis<\/strong> the axis of a hyperbola that includes the foci and has the vertices as its endpoints","rendered":"
Key Equations<\/h2>\n
\n\n
\n
Hyperbola, center at origin, transverse axis on x<\/em>-axis<\/td>\n
A hyperbola is the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the difference of the distances between [latex]\\left(x,y\\right)[\/latex] and the foci is a positive constant.<\/li>\n
The standard form of a hyperbola can be used to locate its vertices and foci.<\/li>\n
When given the coordinates of the foci and vertices of a hyperbola, we can write the equation of the hyperbola in standard form.<\/li>\n
When given an equation for a hyperbola, we can identify its vertices, co-vertices, foci, asymptotes, and lengths and positions of the transverse and conjugate axes in order to graph the hyperbola.<\/li>\n
Real-world situations can be modeled using the standard equations of hyperbolas. For instance, given the dimensions of a natural draft cooling tower, we can find a hyperbolic equation that models its sides.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
center of a hyperbola<\/strong> the midpoint of both the transverse and conjugate axes of a hyperbola<\/p>\n
conjugate axis<\/strong> the axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints<\/p>\n
hyperbola<\/strong> the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the difference of the distances between [latex]\\left(x,y\\right)[\/latex] and the foci is a positive constant<\/p>\n
transverse axis<\/strong> the axis of a hyperbola that includes the foci and has the vertices as its endpoints<\/p>\n\n\t\t\t \n\t\t\t