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.


If I plot a 95% ellipse for a bivariate normal distribution, it might look like the plot below.

When I take a vertical slice through that distribution, I might get a slice like the lighter red line, a, in the center, or I might get a slice like the darker red line, b, on the right.  It looks like a is longer than b (and it is).  That is, the vertical spread from the bottom to the top of the ellipse at a given point on $X$ changes as you move from side to side.  This is simply not the same as the conditional variance.  As a first attempt to understand the bivariate normal and the idea of homoscedasticity, just looking at the vertical spread is reasonable, but it isn't quite right.  It's simply not the case that the length of those lines are the variances of the conditional distributions of $Y$ given $X=x_i$.
With a bivariate normal, you will have more data, and more density in the center (either from side to side, or equally, from top to bottom) than at the extremes.  Where there is more data, you will have more extreme values.  For instance, only 5% will be $>|2|$ SD's from the mean; where you have 100 data, that would be 5, but where you have 1000 data, that will be 50.  The result is that the density is higher with more data and it looks like it is spreading out further, but in both cases, the variance is the same.  To illustrate, consider the very simple simulation below.  Even though the standard deviation is the same, with more data, the value at the 2.5th percentile is further out:
set.seed(1)  # makes this reproducible
quantile(sort(rnorm( 200, mean=0, sd=1)), probs=.025)
#      2.5% 
# -1.641215 
set.seed(1)
quantile(sort(rnorm(2000, mean=0, sd=1)), probs=.025)
#      2.5% 
# -2.092716 

