Sketch and identify the surface

[goonking]

Homework Statement

9x² − 18x + 4z²− 24z − y² + 45 = 0

Homework Equations

The Attempt at a Solution

so let's 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)?

 

[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.

 

[Mark44]

Homework Statement

9x² − 18x + 4z²− 24z − y² + 45 = 0

Homework Equations

The Attempt at a Solution

so let's 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

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.

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)?