\"\"

\

The standard form of vertical ellipse is \"\".

\

Where \"\" and \"\".

\

\"\": 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 \"\".

\

\"\".

\

Center : \"\".

\

Foci : \"\".

\

Vertices : \"\".

\

Co-vertices : \"\".

\

Major axis : \"\".

\

Minor axis : \"\".

\

\"\"

\

Make a table of values to sketch the ellipse.

\

The ellipse equation is \"\".

\

Solve for \"\".

\

\"\"

\

\"\".

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\"\" \

\"\"

\
\"\"
\"\" \

\"\"

\
\

\"\"

\

\"\"

\
\"\" \

\"\"

\
\

\"\"

\

\"\"

\
\

Graph :

\

Plot the points obtained in the table.

\

Plot foci, vertices and center of the  ellipse.

\

Graph the ellipse  \"\" :

\

\"\".

\

\"\"

\

Graph of \"\" :

\

\"\".