Parametrize x and y from 2x^2+xy+y^2=4 as one variable "t"

x=sqrt(2)cos(t)-(1/sqrt(8))sint
y=2.1sin(t)-(1/8)cos(t)

This is close but not exact. I've really just been doing guess and check because I have no idea how to solve it.

By completing the square in y,

2x^2 + (y + x/2)^2-x^2/4 = 4 ==>
7/4*x^2 + (y+x/2)^2 = 4 ==>
7/16*x^2 + 1/4*(y+x/2)^2 = 1 ==>
cos^2(t) + sin^2(t) = 1

Let

sqrt(7)/4*x = cos(t)
1/2*(y+x/2) = sin(t)

then, solving for x and y gives

x = 4*cos(t)/sqrt(7)
y = 2*sin(t) - cos(t)/sqrt(7),

and this parameterization will satisfy the equation.