Hi, I am having trouble with contours, is there a procedure to do these?
the question I am working on is when z=c
z=((x^2)+(y^2))/2x
what i tried to do:
c2x=(x^2)+(y^2)
c2x-x^2=y^2
x(2c-x)=y^2
2c-x=(y^2)/x
2c=((y^2)/x)+x
and that is where I got stuck. I cant visualize what is going on here
thanks for any replys
Yes! For any fixed value of c, is the equation of a circle with radius, c, centered on the x-axis at x=c. This circle passes through the origin.
When looked at in a more general way, is a family of such circles.
Therefore, the equation, , describes a pair of oblique circular cones, each with a vertex at
(0, 0, 0) and axis along the line in the x-z plane. One opens upward, the other downward.
You can also look at this as a pair of right elliptical cones, each with a vertex at (0, 0, 0) and axis along the line in the x-z plane. (I haven't figured out the eccentricity of the ellipses.)