In a certain ellipse, the endpoints of the major axis are $(-11,4)$ and $(9,4).$ also, the ellipse passes through the point $(7,7).$ find the area of the ellipse.

End point of Major Axis =(-11,4) and (9,4), as ends points should have same but opposite in sign x coordinate.So, either it should be (-11,4) and (11,4) or (-9,4) and (9,4).

Length of Major axis ,as y coordinates are same.

      = |9-(-9)| or |11-(-11)|

       =18 or 22

Let equation of ellipse be

Equation of ellipse will be

Area of the ellipse in first Quadrant , if coordinates of end points of major axis are (-9,4) and (9,4).

So, Area of Ellipse

     =4 × Area of ellipse in first Quadrant

If, coordinates of end points of major axis is (-11,4) and (11,4), evaluate by same procedure.