# Math Help - graphing a cylinder

1. ## 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

2. Hello, kittycat!

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

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

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

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

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

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