Given a 2D multivariate Gaussian contour lines and a point $x_0$, is it possible to draw the marginal distribution $f(y)=\mathbb{P}((X,Y)=(x,y)|x=x_0)$. From the picture, it seems the mean of the distribution is where the vertical line $x=x_0$ is tangent to the contour lines (why is that?) but is it possible also from the geometry of the contour line to figure out the variance/spread of the marginal?
