we know that
The equation for the eccentricity of an ellipse is
e=c/a
where
e is eccentricity, c is the distance from the foci to the center, and a is the square root of the larger of our two denominators.
To find c, we must use the equation a²−b²=c², where b is the square root of the smaller of our two denominators
case 1)
(x²/2²)+(y-2)²/4²=1
a=4
b=2
c²=16-4----> c=√12
e=c/a----> √12/4----> e=0.8660
case 2)
(x+3)²/5²+(y-1)²/3²=1
a=5
b=3
c²=25-9----> c=√16-----> c=4
e=c/a----> 4/5-----> e=0.80
case 3)
(x-5)²/3²+(y²/7²)=1
a=7
b=3
c²=49-9-----> c=√40
e=c/a-----> √40/7-----> e=0.9035
case 4)
(x-2)²/4²+(y+4)²7²=1
a=7
b=4
c²=49-16-----> c=√33
e=c/a-----> √33/7------> e=0.8207
case 5)
x²/7²+y²/6²=1
a=7
b=6
c²=49-36-----> c=√13
e=c/a-----> √13/7-----> e=0.5151
case 6)
(x-3)²/6²+y²/4²=1
a=6
b=4
c²=36-16-----> c=√20
e=c/a-----> √20/6-----> e=0.7454
case 7)
(x+4)²/5²+(y-5)²/6²=1
a=6
b=5
c²=36-25-----> c=√11
e=c/a-----> √11/6----> e=0.5528
case 8)
x²/7²+(y+7)²/2²=1
a=7
b=2
c²=49-4----> c=√45
e=c/a-----> √45/7----> e=0.9583
the answer is1) x²/7²+y²/6²=1
e=0.51512) (x+4)²/5²+(y-5)²/6²=1
e=0.55283) (x-3)²/6²+y²/4²=1
e=0.74544) (x+3)²/5²+(y-1)²/3²=1
e=0.80005) (x-2)²/4²+(y+4)²7²=1
e=0.82076) (x²/2²)+(y-2)²/4²=1
e=0.86607) (x+4)²/5²+(y-5)²/6²=1
e=0.90358) x²/7²+(y+7)²/2²=1
e=0.9583
