Consider the level surface given by 2x2+5y2+z2=4. Match the slices with their correct plots below.

Question

tkhunny · Answer

That's a lovely ellipsoid, so they better all look like ellipses.

anonymous · Answer

attachment

anonymous · Answer

So how to match

tkhunny · Answer

Well, how's your Analytic Geometry?

Start with this: $\dfrac{x^{2}}{2} + \dfrac{y^{2}}{4/5} + \dfrac{z^{2}}{4} = 1$

Set x = 0 and get: $\dfrac{y^{2}}{4/5} + \dfrac{z^{2}}{4} = 1$
This, you should recognize as an ellipse with the axis in the y-direction of $2/\sqrt{5}$ and the axis in the z-direction of $2$.  Do you see one of those?

Set y = 0 and get: $\dfrac{x^{2}}{2} + \dfrac{z^{2}}{4} = 1$
This, you should recognize as an ellipse with the axis in the x-direction of $\sqrt{2}$ and the axis in the z-direction of $2$.  Do you see one of those?

Continue with this sort of investigation.

anonymous · Answer

It's look like football :DD

tkhunny · Answer

Yes, yes it does.  But today, we're projecting the football onto a plane and examining the cross sections.

anonymous · Answer

Thank you so much, tkhunny! I got the answer!