EllipseStandard Equation Hyperbola

Writing equation of an Writing equation of an EllipseEllipseExample: 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)

x2 + y2

254= 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

x2 + y2

369= 1

.(0,-6)

.(3,0)

Finding the foci of an Finding the foci of an EllipseEllipseExample: Find the foci of the ellipse with the

equation 25x2 + 9y2= 225

25x2 + 9y2= 225225225225

x2 + y2=1259

c2 = a2 - b2

c2 = 25 - 9c2 = 16c = 4

Foci: (0,4) and (0,-4)

Vertices: (0,+/- 5) and (+/- 3,0)

Practice: Find the foci of the ellipse with the

equation x2 + 9y2= 9

PRACTICEPRACTICEGraph and find the Vertices and Foci of the following ellipse

1. 13x2 + 17y2= 221 2. 16x2 + 9y2= 144

Vertices:

Foci:

( ± √17 , 0)( 0 , ± √13 )

( ± 2 , 0)

Standard:

x2 + y2

1317= 1

Vertices:

Foci:

( 0 , ± 4 )( ± 2 , 0 )

(0 , ±√7)

Standard:

x2 + y2

169= 1