Write the equation for the ellipse in standard form?

Question

the length of the semi-major axis is 6 units, and teh foci are located at (0,2) and (8,2)

Answer 1

halfway between foci is the center, (4,2), so we know it's (x-4)²/a² + (y-2)²/b² = 1. semimajor length 6 is a. focus to center distance is 4, so b² + 4² = 6², b² = 36 - 16 = 20. thus
(x-4)²/36 + (y-2)²/20 = 1

Answer 2

foci is located at (h+c, k) and (h-c, k)

h = 4 and k = 2 and c = 4

c^2 = a^2 + b^2
16 = 36 - b^2
b^2 = 20

so the eq is

(x-4)^2 /36 + (y-2)^2/20 = 1