I was wondering if I could receive help on how to sketch the surface (x-2)^2 - y^2 - (z+1)^2 = 0. I'm unsure of where to start, should I calculate the intercepts and estimate the dimensions?
2026-05-06 08:55:24.1778057724
How to sketch a surface
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This is a quadric surface. In particular, it is a degenerate hyperboloid -- a conical surface. The apex is at $(2,0,-1)$. Notice that you can move the negative terms to the other side, $$ (x-2)^2 = y^2 + (z+1)^2 \text{,} $$ showing that for each choice of $x$, you obtain a circle in the plane of points having that $x$ coordinate. This tells us the axis of revolution of the surface is parallel to the $x$ axis (the circles are traced out as $y$ and $z$ vary).