Match the equation with its graph (labeled I-VIII). Give reasons for your choice.
$ y^2 = x^2 + 2z^2 $
So for 26 we want to match the equation with its graph. Um, and in this case, the equation that we have the graph that were given is y squared equals X squared plus two z squared. So what we can do is we can use traces. So if we let Z equal K, then what will end up getting? Is that why squared minus X squared equals two k squared. So these traces are obviously hyperbole as so. What that means is that when we let Z be constant, the X and Y plane is going to be is going to show hyperbole eyes. Then if y equals K um, so we just have the xz plane. Then what we end up getting is that k squared equals X squared plus two z squared. And this would obviously be ellipses then lastly, we let x equal k and we end up getting y squared minus two z squared equals k squared. And these are also hyperbole us. So, based on this, looking at the different traces that we have, um, we see that 12 and three are possible traces, But since 000 is a point on this surface, only one is going to have it. So our answer for this graph is going to be one mhm.