Precalculus 2014

 PAGE: 438 SET: Exercises PROBLEM: 1

The standard form of vertical ellipse is .

Where

,

,

: length of semi major axis,

: length of semi minor axis,

Center : ,

Foci : ,

Vertices : ,

Co-vertices : ,

Major axis : ,

Minor axis : .

The ellipse equation is .

Rewrite the above equation as .

Compare the equation with .

and .

.

Use these values to determine the characteristics of the ellipse.

Since , it is a vertical ellipse.

Center : .

Foci : .

Vertices : .

Co-vertices : .

Major axis : .

Minor axis : .

Graph the center, vertices, foci, and axes.

Make a table of values to sketch the ellipse.

The ellipse equation is .

Solve for .

.

Plot the points and sketch the ellipse.

Graph :

Graph of :

.

Graph of :

.

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