Shapes of surfaces in R^3
I have to describe the shapes given by some formulas, would this be the way to do it ,I'll do it with one of my problems:
(the x2 and y2 below are meant to be x squared and y squared)
f(x,y) = 2 √ (x2 + y2)
So to get a projection on the Y-Z axis I put x=0 then z=2y
Same for the X-Z axis, if y=0 then z=2x So this forms 2 straight lines where the z value is always double the x or y value so all of this together gives a cone along the z axis.
Then we must find the contour lines, so if we put z=1 then this is a circle with a radius of 1/4
Similarly if z=2 this is a circle with radius 1 and so on.
So this definitely gives a cone starting at the origin and formed along the z axis.
Is that right?