# graphing a cylinder

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• Jul 6th 2007, 01:19 AM
kittycat
graphing a cylinder
Hi,

Please teach me how to graph a cylinder ( please show me the step of graphing). Thank you very much.

4x^2 + y^2 = 9
• Jul 6th 2007, 04:10 AM
Soroban
Hello, kittycat!

Quote:

Please teach me how to graph a cylinder: .$\displaystyle 4x^2 + y^2 \:= \:9$

Since $\displaystyle x$ is not in the equation, $\displaystyle z$ is unrestricted.
. . The $\displaystyle z$-values are on $\displaystyle (-\infty,\,\infty)$
The graph extends "up" and "down" infinitely.

When $\displaystyle z=0$, we have the trace of the cylinder on the $\displaystyle xy$-plane
. . . . . the "floor" of the coordinate system.

This trace is: .$\displaystyle 4x^2 + y^2 \:=\:9\quad\Rightarrow\quad\frac{x^2}{\frac{9}{4}} + \frac{y^2}{9} \:=\:1$

This is an ellipse with major axis 6 in the $\displaystyle y$-direction
. . and minor axis 3 in the $\displaystyle x$-direction.

Sketch this ellipse on the $\displaystyle xy$-plane (the "floor")
. . then draw the cylinder "straight up" and "straight down".