Given a question to graph:
x^2 + 4y^2 = 16
I would assume its a 2D Plot. My textbook assumes otherwise and treats it as a trace.
This is how the equation looks like when plotted.
x^2 + 4y^2 = 16
My question is - is the 3D plot of x^2 + 4y^2 = 16 the same as the 2D plot of x^2 + 4y^2 = 16 except one is parallel to the plane and thats it? What distinguishes them? In the future if Im asked to draw a cylinder plane what would be the proper equation for it?
$x^2+4y^2 = 16$ is the same thing as saying that $x^2+4y^2+0z=16$. So $z$ will not affect your graph, but now you can graph this equation in $3$ dimensions.