Question

Describe the surfaces defined by the equation f = const, where f = x^2 + 4y^2 Hint: A good way to do this is to plot the surfaces parametrically using a program like Mathematica (in Mathematica, use ParametricPlot3D). In order to parametrize this function, picture it this way: x^2 + 4y^2= constant = C^2 (saying that this constant is C2 is a matter of convenience, you'll see why in the next step) x^2/C^2 + 2^2y^2/C^2 = 1 now we define 2 new coordinates: u = x/C, v = 2y/C. So we have: u^2+v^2=1 Now this curve is very similar to one we have already seen, that we can parametrize as a function of a parameter ?. After parametrizing u=u(?) and v=v(?), find x=x(?) and y=y(?), and you are ready to plot it. Elliptical cylinder Cylinder Ellipsoid of revolution Sphere

          Describe the surfaces defined by the equation f = const, where f = x^2 + 4y^2

Hint: A good way to do this is to plot the surfaces parametrically using a program like Mathematica (in Mathematica, use ParametricPlot3D).
In order to parametrize this function, picture it this way:
x^2 + 4y^2= constant = C^2 (saying that this constant is C2 is a matter of convenience, you'll see why in the next step)
x^2/C^2 + 2^2y^2/C^2 = 1
now we define 2 new coordinates: u = x/C, v = 2y/C. So we have:
u^2+v^2=1
Now this curve is very similar to one we have already seen, that we can parametrize as a function of a parameter ?. After parametrizing u=u(?) and v=v(?), find x=x(?) and y=y(?), and you are ready to plot it.
Elliptical cylinder
Cylinder
Ellipsoid of revolution
Sphere

Describe the surfaces defined by the equation f = const, where f = x^2 + 4y^2

Hint: A good way to do this is to plot the surfaces parametrically using a program like Mathematica (in Mathematica, use ParametricPlot3D).
In order to parametrize this function, picture it this way:
x^2 + 4y^2= constant = C^2 (saying that this constant is C2 is a matter of convenience, you'll see why in the next step)
x^2/C^2 + 2^2y^2/C^2 = 1
now we define 2 new coordinates: u = x/C, v = 2y/C. So we have:
u^2+v^2=1
Now this curve is very similar to one we have already seen, that we can parametrize as a function of a parameter ?. After parametrizing u=u(?) and v=v(?), find x=x(?) and y=y(?), and you are ready to plot it.
Elliptical cylinder
Cylinder
Ellipsoid of revolution
Sphere

Added by Lisa M.

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