Conic Sections - Ellipses Chapter 8, Section 2

About Ellipses Definition Focus – one of the fixed points The set of all points in a plane such that the sum of the distances from two fixed points is a constant. Focus – one of the fixed points Focal axis – the line through the foci Center – the point on the focal axis midway between the foci Vertex – endpoint of the major and minor axis

About Ellipses, continued… Major axis: Length is 2a Is horizontal if x has the larger denominator Is vertical if y has the larger denominator minor axis: Length is 2b Focal radii – segment joining each focus to a point on the ellipse Sum of lengths is 2a Is the distance from the center to a focus

Horizontal Ellipses Center: (h,k) Focus: (h+c,k) (h-c,k) Major axis: y=k Major axis vertices: (h+a,k) (h-a,k) Minor axis: x=h Minor axis vertices: (h, k+b) (h, k-b)

Vertical Ellipses Center: (h,k) Focus: (h,k+c) (h,k-c) Major axis: x=h Major axis vertices: (h,k+a) (h,k-a) Minor axis: y=k Minor axis vertices: (h+b,k) (h-b,k)

Examples – find the center, foci, vertices, major and minor axis

Examples – write the equation in standard form

Classwork/Exit Slip Find the center, foci, vertices, major and minor axis: Write the equation of the ellipse if the foci are at (-2,0) and (2,0) and a=7 Homework: Page 652, #21, 24, 27, 33, 45, 46 Find vertices and foci on #45, 46