Ellipse Standard Equation Hyperbola. Writing equation of an Ellipse Example: write the standard form on an ellipse that has a vertex at (0,5) and co-vertex.

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Presentation transcript:

Ellipse Standard Equation Hyperbola

Writing equation of an Ellipse Example: write the standard form on an ellipse that has a vertex at (0,5) and co-vertex (2,0) and the center at the origin. (0,5). (2,0) x 2 + y = 1 Practice: write the standard form on an ellipse that has a vertex at (3,0) and co-vertex (0,-6) and the center at the origin x 2 + y = 1. (0,-6). (3,0)

Finding the foci of an Ellipse Example: Find the foci of the ellipse with the equation 25x 2 + 9y 2 = x 2 + 9y 2 = x 2 + y 2 = c 2 = a 2 - b 2 c 2 = c 2 = 16 c = 4 Foci: (0,4) and (0,-4) Vertices: (0,+/- 5) and (+/- 3,0) Practice: Find the foci of the ellipse with the equation x 2 + 9y 2 = 9

PRACTICE Graph and find the Vertices and Foci of the following ellipse 1. 13x y 2 = x 2 + 9y 2 = 144 Vertices: Foci: ( ± √17, 0 ) ( 0, ± √13 ) ( ± 2, 0 ) Standar d: x 2 + y = 1 Vertices: Foci: ( 0, ± 4 ) ( ± 2, 0 ) (0, ±√7 ) Standar d: x 2 + y = 1