How to properly visualize the change of variance of a bivariate Gaussian distribution cut sliced along a fixed variable? I'm trying to understand the basics of Gaussian Distribution. I struggle to visualice how the variance of the conditional probability of say P (Y|X) changes when X is fixed (given X and Y have a joint gaussian distribution). So, I have two pictures , in picture A from many sources shows that the variances dont change but the mean does.  But it seems reasonable to me also to consider the conditional as a cut of de bivariate along one axis but now the variances does change, why is it so?  I'm I  wrongly thinking Picture B is the conditional?
Picture A

[Picture updated thanks to contribution]
Picture B
Cuts along one variable.  It seems that the variance (spread of black lines) increases or decreases according to a fixed X.


In the spirit of my original post at What is the intuition behind conditional Gaussian distributions?, we should look at the situation and consider it geometrically.
Begin with the bottom illustration, which slices the bivariate density in the vertical direction (that is, through fixed values of $x$):

Here is a plot of the slices through the positive $x$ values (those closest to you in the previous image) on common axes:

In this example, because the correlation is negative, as $x$ increases (1) the center of the slice shifts leftwards and (2) the height decreases.  The height is the original bivariate density.  I use the original color scheme to emphasize this.
You want to visualize the conditional densities: these represent the distribution of the response, $y,$ for any given value of $x.$  They are obtained by scaling the slices in the vertical (density) direction to give them a unit area, which is a basic requirement of any probability density.  Here is an example of scaling the slice through $x=1.5$ appearing at the very front edge of the original graphic:

The arrows show how each original point is moved to a new point.  The colors now represent the (new) conditional density while the heights represent both the original bivariate density and the conditional density (ignoring the fact that the two densities use different units of measurement!).
The conditional variance describes the spread of the conditional density.  Evaluate the spread by examining the rescaled densities.  Here is the plot of the original slices, all rescaled into conditional densities:

(The color continues to depict the original bivariate density.)
It is now evident that (in this example) all the conditional distributions are translates of a common distribution.  Clearly they all have the same spread, whence their variances are equal.
