a b Center at( h,k ) An ellipse with major axis parallel to x -axis c Definition

Important Idea a>ba>b a b ( h,k ) c

Definition The standard form of the equation of an ellipse when the major axis is parallel to the x -axis

An ellipse with major axis parallel to y -axis a b Center: at ( h,k ) c Definition

The standard form of the equation of an ellipse when the major axis is parallel to the y -axis

Important Idea The direction of the major axis is determined by the larger denominator. The larger denominator is always a 2 in the standard equation. If the larger denominator is under the x term, the ellipse is “fat”; if the larger denominator is under the y term, the ellipse is “skinny”

Try This For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.

Solution Center:(0,-4) Foci: Vertices: (±6,-4) Minor Axes Ends(0,1),(0,-9)

Try This Write an equation of the ellipse with Foci (3,2) and (3,-4) and whose major axes is 14 units long.

Solution

How is the “roundness” of an ellipse measured?

Try This For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.

Solution Center:(3,2) Foci: Vertices: (-2,2) (8,2) Minor Axes Ends(3,3),(3,1)

Another For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.

Solution Center:(2,-3) Foci: Vertices: (6,-3) (-2,-3) Minor Axes Ends(2,-6),(2,0)