Find an equation in standard form

Question

Find an equation in standard form for the ellipse with center at (8, 4), horizontal major axis of length 6 and passes through the point (10, 2).

Answer 1

(x -8)^2/a^2 + (y-4)^2/b^2 = 1

semi major axis = 3 = a or b depending on which is the major axis

goes through the point (10,2) which is 2 units above the center and 2 units to the left of the center

if horizontal axis is the major axis then

(10-8)^2/9 + (2-4)^2/b = 1

4/9 -1 = -4/b

5/9 = 4/b

b = 36/5 and the ellipse is

(x-8)^2/9 + (y-4)^2/(36/5)^2 = 1

but if vertical axis is the major axis then

(x-8)^2/a^2 + (y-4)^2/9 = 1, plug in x=10, y=4 and solve for a

4/a^2 + 4/9 = 1

4/a^2 = 1-4/9 = 5/9

a^2 = 36/5 and the ellipse is

(x -8)^2/(36/5)^2 + (y-4)^2/9 = 1

but 36/5 = 7.2 which is larger than 3, so 3 can't be the semi major axis regardless whether it's the vertical or horizontal axis

there's a problem with the problem, as there is no solution that satisfies the given requirements