What is The equation of an Ellipse Definition

What is The equation of an Ellipse

Definition An ellipse is the locus (set) of all points such that the sum of the distances from two points called foci is constant.

P 1(x 1, y 1) Vertex Minor Axis Focus Major Axis Center Focus Vertex

Definition b a c Center at(h, k) An ellipse with a horizontal major axis.

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

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

An ellipse with a vertical major axis. Definition a c b Center: at (h, k)

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

Important Idea The of the majoris If thedirection larger denominator axis is determined by the under the x term, the larger denominator. The ellipse is “fat”; if theislarger denominator 2 always a in the standard denominator is under the y equation. 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: (2, -3) Foci: Vertices: (6, -3) (-2, -3) Minor Axes Ends(2, -6), (2, 0)

Quick Summary • Describe the meanings of the values a, b, c, h & k. • What is wrong? a=5 ; b=6