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\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>\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>\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>\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>\n<\/ul>
Glossary<\/h2>\n
center of an ellipse<\/dt>
the midpoint of both the major and minor axes<\/dd><\/dl>
conic section<\/dt>
any shape resulting from the intersection of a right circular cone with a plane<\/dd><\/dl>
ellipse<\/dt>
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<\/dd><\/dl>
foci<\/dt>
plural of focus<\/dd><\/dl>
focus (of an ellipse)<\/dt>
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<\/dd><\/dl>
major axis<\/dt>
the longer of the two axes of an ellipse<\/dd><\/dl>
minor axis<\/dt>
the shorter of the two axes of an ellipse<\/dd><\/dl>","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
\n
center of an ellipse<\/dt>\n
the midpoint of both the major and minor axes<\/dd>\n<\/dl>\n
\n
conic section<\/dt>\n
any shape resulting from the intersection of a right circular cone with a plane<\/dd>\n<\/dl>\n
\n
ellipse<\/dt>\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<\/dd>\n<\/dl>\n
\n
foci<\/dt>\n
plural of focus<\/dd>\n<\/dl>\n
\n
focus (of an ellipse)<\/dt>\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<\/dd>\n<\/dl>\n
\n
major axis<\/dt>\n
the longer of the two axes of an ellipse<\/dd>\n<\/dl>\n
\n
minor axis<\/dt>\n
the shorter of the two axes of an ellipse<\/dd>\n<\/dl>\n\n\t\t\t \n\t\t\t