2 Answers

2x^2 + 6y^2 = 12, ie., (x/rt6)^2 + (y/rt2)^2 = 1, ie., (x/a)^2 + (y/b)^2 = 1, where a = rt6, b = rt2. Center = (0,0),
major vertices are ([+/]a,0) = ([+/]rt6,0), minor vertices are (0,[+/]b) = (0,[+/]rt2), foci are ([+/]c,0) = ([+/]2,0).
Note: c^2 = a^2 – b^2 = (rt6)^2 – (rt2)^2 = 62 = 4 & c = 2.

You mean this?
2x² + 6y² = 12
Try writing it in standard form. That helps show many of the parameters.
2x² + 6y² = 12
x²/6 + y²/2 = 1
(x – 0)²/√(6)² + (y – 0)²/√(2)² = 1
center: (0, 0)
semimajor (horizontal): √(6)
semiminor (vertical): √(2)
focal distance = √(6 – 2) = 2
major vertices: (√(6), 0), (√(6), 0)
minor vertices: (0, √(2)), (0, √(2))
foci: (2, 0), (2, 0)