Question 74533
Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).


The length of the major axis would be 12 units. 2a=12. a=6.

The length of the minor axis is 8 units. 2b=8. b=4.

You're right up to here, but this ellipse is not centered at the origin (0,0).
Notice that the x coordinate of the end points of the major axis is 1.  
The y coordinate of the end points of the minor axis is 0.
That means that the center is (1,0).  
This can be seen if you draw your ellipse.
The formula for an ellipse with a vertical major axis is:
{{{highlight((x-h)^2/b^2+(y-k)^2/a^2=1)}}}
major axis=2a
minor axis=2b
Center=(h,k)
You found that a=6 and b=4 and now you know that (h,k)=(1,0)
{{{(x-1)^2/4^2+(y-0)^2/6^2=1}}}
{{{highlight((x-1)^2/16+y^2/36=1)}}}
Happy Calculating!!!!