For this problem. We've been given a function in three variables X squared plus three y squared plus five z squared. And what we want to do for this problem is to find describe the level surfaces of this function. Now level surfaces of a function is we take this function and we said it equal to K some constant. So we want to know what values of X, Y and Z We can change them as much as we want. We want the whole functions value to remain constant, and hopefully we can change K two different constant values. And we can see what's happening to our function at different points. Um, it's a way of sometimes helping Thio visualize Ah three d shape a little bit more clearly. So let's see what we have here. Um, if I take this function that set equal to K, if I had a two dimensional function on, I'm just gonna take the x and y here. Let's say I had a two dimensional function equal decay where I had everything is positive and I have x squared and y squared. This is the equation of an ellipse. It's a little bit easier to see if we set it equal toe one like we would normally do for in the lips because that would give me X squared over K plus y squared three y squared over K. And if I want to put everything in the denominator like we often have feel y squared over B B squared, that would be my lips equation. Okay, so that's the two dimensional version. This three dimensional version is very similar again. Let me divide everything by K just you might be able to see this a little bit easier. X squared over K. That's why squared over K over three and I could do the same thing here. Z squared over K over five now. I wouldn't typically leave it with that fraction in the denominator, but it helps to see what's holding on with our lips. So this is an ellipse. Um, my biggest denominator is K K, which is under the X. So my major access for this ellipse oId this three dimensional lip shape is going to be along the X axis. And as I change k, this is going thio grow shrink, become different things. If I got if I put k equaling 20 then this kind of devolves into a single point right at the origin. As I get K bigger and bigger. My lips was going to expand, but these were going to be nested ellipse Lloyd's, um, as whenever I set them equal to K for these level surfaces.