SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics. Center: (3, −8); a = 8c; foci: (3, −9), (3, −7)

Notice that the foci lie on vertical line x = 3.


It means that the major axis of the ellipse is vertical  x= 3, parallel to y-axis,

and the minor axis is horizontal y= -8, parallel to x-axis.


The distance between the foci is  2c = -7 - (-9) = 2;  hence, the linear eccentricity is half of this distance c = 2/2 = 1.


Further, the major semi-axis  a = 8c = 8;  hence, the minor semi-axis is  b =  =  = .


Now we are ready to write the standard form equation of the ellipse


     +  = 1,

or

     +  = 1.