Graph and Write Equations of Elllipses

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Presentation transcript:

Graph and Write Equations of Elllipses Section 9.4 Graph and Write Equations of Elllipses

California Standard: 16.0: Students demonstrate and explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Graph and write equations of ellipses.

Def: An ellipse is the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant. Standard Equation of an Ellipse with Center at the Origin y y x x

EXAMPLE 1: Graph . Identify the vertices, co-vertices and foci of the ellipse.

U-TRY#1: Graph the equation. Identify the vertices, co-vertices, and foci of the ellipses. A) B) C)

EXAMPLE 2: Write an equation of the ellipse that has a vertex at (0,4), a co-vertex at (-3,0), and center at (0,0).

EXAMPLE 3: Write an equation of an ellipse that has a major horizontal axis of 400 and a minor vertical axis of 200.

EXAMPLE 4: Write an equation of the ellipse that has a vertex at (- 8,0), a focus at (4,0), and center at (0,0).

U-TRY#2: Write an equation of the ellipse with the given characteristics and center at (0,0) Vertex: (7,0); co-vertex: (0,2) Vertex: (0,6); co-vertex (-5,0) Vertex: (0,8); focus: (0,-3) Vertex: (-5,0); focus: (3,0)

HOMEWORK Sec 9.4 WS