Question 74446
MY ORIGINAL ANSWER TO THIS QUESTION HAD THE MAJOR AND MINOR AXES REVERSED.  THIS HAS BEEN CORRECTED.  I APOLOGIZE FOR THE ERROR.


A general equation for an ellipse centered at (h,k), with the major axis parallel to the y axis is:


{{{(((x-h)^2)/b^2)+(((y-k)^2)/a^2)=1}}}


For your case:

the ellipse is centered at (1,0),, the intersection of the major and minor axes

the length of the major axis (a) is 12,, the distance between (1,6) and (1,-6)

the length of the minor axis (b) is 8,, the distance between (5,0) and (-3,0)


So the equation is:


{{{(((x-1)^2)/64)+((y^2)/144)=1}}}