The equation of the surface in cylindrical coordinates:

i) What is the equation in perpendicular coordinates?
ii) Write it name?

My try:
I put these in the original equation:


Like a sphere? I'm stuck here
I request your help

  • 2
    $\begingroup$ It is an ellipsoid. $\endgroup$
    – Math Lover
    Jan 31, 2021 at 11:16
  • $\begingroup$ Center at $(2, -4, 3)$ and $a = \sqrt2, b = \sqrt2, c = 1$ in equation $(x-h)^2 / a^2 + (y-k)^2/b^2 + (z-l)^2 / c^2 = 1$. $\endgroup$
    – Math Lover
    Jan 31, 2021 at 11:24

1 Answer 1


You have a mistake in a sign in your last step: $$(x-2)^2+(y+4)^2{\color{red}-}2(z-3)^2=2.$$ So the surface is a hyperboloid of one sheet (see https://en.wikipedia.org/wiki/Quadric): $$\frac{(x-2)^2}{(\sqrt{2})^2}+\frac{(y+4)^2}{(\sqrt{2})^2}-\frac{(z-3)^2}{1^2}=1.$$

  • $\begingroup$ Thank you for reply. But, you said it is "hyperboloid". If the denominator of (z-3) is "1", then isn't it "Elliptic paraboloid"? $\endgroup$
    – gunza
    Jan 31, 2021 at 12:31
  • 1
    $\begingroup$ For that it should be $(x-2)^2/2+(y+4)^2/2+(z-3)=0$ without the square in $(z-3)$. $\endgroup$ Jan 31, 2021 at 12:37

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