# Sketch and identify the surface

1. Sep 18, 2015

### goonking

1. The problem statement, all variables and given/known data
9x2 − 18x + 4z2− 24z − y2 + 45 = 0

2. Relevant equations

3. The attempt at a solution
so lets start with the zy trace, setting x=0
we are left with:

4z2 - 24z - y2 = -45

completeing the square gives :

4z2 - 24z + 144 - y2 = -45 +144

4(z-12)2 - y2 = 99

divide both sides by 99

4(z-12)2 /99 - y2/99 = 1

so the center is at (12,0)? is a = sqrt of (4/99)?

2. Sep 18, 2015

### davidmoore63@y

Don't be too quick to set x=0. Keep all the variables, and complete the square in both x and z and see what you get. Be careful on the algebra in completing the square, the above effort seems incorrect.

3. Sep 18, 2015

### Staff: Mentor

You have a mistake in the line above. Completing the square is easier if you take out the common factors first.

In addition to your work in finding the various traces, you should complete the square in x and z in the original equation, as David Moore advises.