Table of Contents Ellipse - Finding the Equation Recall that the two equations for the ellipse are given by... Horizontal EllipseVertical Ellipse.

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Presentation transcript:

Table of Contents Ellipse - Finding the Equation Recall that the two equations for the ellipse are given by... Horizontal EllipseVertical Ellipse

Table of Contents Slide 2 Ellipse - Finding the Equation Summary of meanings of a, b, h, and k: The end points of the minor axis are b units from the center. The vertices are a units from the center on the major axis. The center is at C(h, k). The foci are c units from the center on the major axis.

Table of Contents Slide 3 Ellipse - Finding the Equation Example 1: Find the equation of the ellipse with the given vertices and foci... The first step is to plot these points on a coordinate plane.

Table of Contents Slide 4 Ellipse - Finding the Equation The center will be the midpoint of the line segment joining the vertices (also the foci)... The distance from the center to a vertex is a = 6. The distance from the center to a focus is c = 4.

Table of Contents Slide 5 Ellipse - Finding the Equation Using the formula... the value of b can be found.

Table of Contents Slide 6 Ellipse - Finding the Equation Summary: Since the vertices are vertical, the ellipse is vertical... and the equation is...

Table of Contents Slide 7 Ellipse - Finding the Equation Example 2: Find the standard form of the ellipse given by... Solution:

Table of Contents Slide 8 Ellipse - Finding the Equation The standard form of the ellipse is...

Table of Contents Ellipse - Finding the Equation