eliminating the parameter

All we need to do is make use of the identity

sin^{2} t + cos^{2} t = 1

To do this we will square both parametric equations to get

x^{2} = 9 sin^{2} t and y^{2} = 4 cos^{2 }t

x^{2}/9 = sin^{2} t and y^{2}/4 = cos^{2} t

Now wee add the two equations

x^{2}/9 + y^{2}/4 = sin^{2} t + cos^{2} t

(x/3)^{2} + (y/2)^{2} = 1