Question 459550
write an equation of an ellipse with co-vertices of (-3,0) and (3,0), and vertices (0,-5). Graph the ellipse
<pre>
We plot the 2 vertices and the 2 co-vertices: 

{{{drawing(400,400,-7,7,-7,7, graph(400,400,-7,7,-7,7),
circle(-3,0,.1), circle(3,0,.1),circle(0,-5,.1), circle(0,5,.1) )}}}

We sketch in the graph of the ellipse:

{{{drawing(400,400,-7,7,-7,7, graph(400,400,-7,7,-7,7),
arc(0,0,6,-10),
circle(-3,0,.1), circle(3,0,.1),circle(0,-5,.1), circle(0,5,.1) )}}}

The equation of an ellipse with center (0,0) which has its major
axis vertical is

xｲ   yｲ
覧 + 覧 = 1
bｲ   aｲ

Where "a" represents the number of units from the center 
to either of it vertices and "b" represents the number of
units from the center to either of its co-vertices.  So
a = 5 and b = 3 and the equation is:

xｲ   yｲ
覧 + 覧 = 1
3ｲ   5ｲ

or

xｲ   yｲ
覧 + 覧 = 1
9    25

Edwin</pre>