The joint density of x = (x1, x2) is shown as its elliptical level sets. Observing x2 = w restricts you to one horizontal line: drag it. The density along that line, rescaled to have area one, is the conditional density p(x1 | x2 = w) drawn below. It is again Gaussian, its mean moves affinely with w along the orange line, and its variance does not depend on w at all.
Below: the density along the red line. Dragging the line slides this curve sideways without ever changing its width.