SOLUTION: Find the center,foci,vertices and covertices of the ellipse with the given equation. 9x^2+16y^2-126x+64y=71

 =   --->

 =   --->

 = ,

 = ,

 = ,

 = ,      ( <--- next divide both sides by 676 =  )

 = 1,  or

 = 1.

The center of the ellipse is the point  (7,-2).

The semi-major axis is a = .

The semi-minor axis is b =  = 13/2.   (Notice that a > b. The major axis is horizontal, and the ellipse is wider than tall).

Two vertices in horizontal directions are  (,)  and  (,).

Two vertices in vertical directions are  (,)  and  (,).

The linear eccentricity is c =  =  =  =  =  = .

The foci are  (,)  and  (,).