Is it possible to create a mesh plot out of a 2D Taylor expansion series?

x0 = 2;
y0 = 2;

real = exp(-x0^2-1/4*x0*y0-1/8*y0^2);
syms x y
a = linspace(-5,5,50);
b = linspace(-10,10,50);
[X,Y]=meshgrid(a,b);
taylor(exp(-x^2-1/4*x*y-1/8*y^2),[x y], [2 2])

I don't know much about how the mesh function works, or the Taylor Expansion function for that matter. I need to create a mesh and contour plot of a 2D taylor expansion about the point 2,2 for ''exp(-x^2-1/4*x*y-1/8*y^2)''. I need to somehow make a matrix out of what the taylor function is spitting out.

Any help on this would be great!