Hello could anyone please tell me if the following answers to the problems are correct? if they are not could you please show me where I went wrong? Thanks!

1) Find the center, foci, vertices, and eccentricity of the of the ellipse and sketch graph of the follwing equation:

16x^(2) + 25y^(2) - 64x + 150y + 279= 0

Solution:

Center- (2, -3)

Vertices- ( 2 + 0.791, -3) ; (2 -0.791, -3)

Foci- ( 2 + 0.474, -3) ; (2 -0.474, -3)

eccentricity-0.474

0.791

2) Find the equation of each ellipse given the following:

a) Vertices- (0, 2) ; (4, 2)

Eccentricity-1

2

Solution:(x - 2)^(2)+(y - 2)^(2)= 1

4 3

b) Foci- (0, 5) ; (0, -5)

Major axis length- 14

Solution:x^(2)+y^(2)= 1

24 49

c) Center- (1, 2)

major axis- vertical

points on the ellipse: (1, 6) ; (3, 2)

Solution:(x -1)^(2)+(y -2)^(2)= 1

4 16