{"id":2340,"date":"2016-11-03T20:31:29","date_gmt":"2016-11-03T20:31:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&p=2340"},"modified":"2025-10-15T22:37:32","modified_gmt":"2025-10-15T22:37:32","slug":"summary-the-ellipse","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/chapter\/summary-the-ellipse\/","title":{"raw":"Summary: The Ellipse","rendered":"Summary: The Ellipse"},"content":{"raw":"
An ellipse is the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the sum of their distances from two fixed points is a constant. Each fixed point is called a focus (plural: foci).<\/li>\r\n \t
When given the coordinates of the foci and vertices of an ellipse, we can write the equation of the ellipse in standard form.<\/li>\r\n \t
When given an equation for an ellipse centered at the origin in standard form, we can identify its vertices, co-vertices, foci, and the lengths and positions of the major and minor axes in order to graph the ellipse.<\/li>\r\n \t
When given the equation for an ellipse centered at some point other than the origin, we can identify its key features and graph the ellipse.<\/li>\r\n \t
Real-world situations can be modeled using the standard equations of ellipses and then evaluated to find key features, such as lengths of axes and distance between foci.<\/li>\r\n<\/ul>\r\n
Glossary<\/h2>\r\ncenter of an ellipse<\/strong>\r\n\r\n \r\n\r\nthe midpoint of both the major and minor axes\r\n\r\nconic section<\/strong>\r\n\r\n \r\n\r\nany shape resulting from the intersection of a right circular cone with a plane\r\n\r\nellipse<\/strong>\r\n\r\n \r\n\r\nthe set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the sum of their distances from two fixed points is a constant\r\n\r\nfoci<\/strong>\r\n\r\n \r\n\r\nplural of focus\r\n\r\nfocus (of an ellipse)<\/strong>\r\n\r\n \r\n\r\none of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point [latex]\\left(x,y\\right)[\/latex] on the ellipse is a constant\r\n\r\nmajor axis<\/strong>\r\n\r\n \r\n\r\nthe longer of the two axes of an ellipse\r\n\r\nminor axis<\/strong>\r\n\r\n \r\n\r\nthe shorter of the two axes of an ellipse\r\n","rendered":"
An ellipse is the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the sum of their distances from two fixed points is a constant. Each fixed point is called a focus (plural: foci).<\/li>\n
When given the coordinates of the foci and vertices of an ellipse, we can write the equation of the ellipse in standard form.<\/li>\n
When given an equation for an ellipse centered at the origin in standard form, we can identify its vertices, co-vertices, foci, and the lengths and positions of the major and minor axes in order to graph the ellipse.<\/li>\n
When given the equation for an ellipse centered at some point other than the origin, we can identify its key features and graph the ellipse.<\/li>\n
Real-world situations can be modeled using the standard equations of ellipses and then evaluated to find key features, such as lengths of axes and distance between foci.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
center of an ellipse<\/strong><\/p>\n
<\/p>\n
the midpoint of both the major and minor axes<\/p>\n
conic section<\/strong><\/p>\n
<\/p>\n
any shape resulting from the intersection of a right circular cone with a plane<\/p>\n
ellipse<\/strong><\/p>\n
<\/p>\n
the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the sum of their distances from two fixed points is a constant<\/p>\n
foci<\/strong><\/p>\n
<\/p>\n
plural of focus<\/p>\n
focus (of an ellipse)<\/strong><\/p>\n
<\/p>\n
one of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point [latex]\\left(x,y\\right)[\/latex] on the ellipse is a constant<\/p>\n
major axis<\/strong><\/p>\n
<\/p>\n
the longer of the two axes of an ellipse<\/p>\n
minor axis<\/strong><\/p>\n
<\/p>\n
the shorter of the two axes of an ellipse<\/p>\n\n\t\t\t \n\t\t\t