Consider the level surface given by
x2−y2+z2=2. Draw a picture for the following:

1. Slice for y=2
2. Slice for x=1
3. Slice for y=0
4. Slice for x=2

Question

Consider the level surface given by
x2−y2+z2=2. Draw a picture for the following:

1. 	Slice for y=2
 	2. 	Slice for x=1
 	3. 	Slice for y=0
 	4. 	Slice for x=2

dumbcow · Answer

1. circle of radius sqrt(6) in x-z plane 
2. hyperbola in y-z plane opening in z direction
3. circle of radius sqrt(2) in x-z plane 
4. hyperbola in y-z plane opening in y direction

anonymous · Answer

How do you know which way the hyperbola opens?

dumbcow · Answer

whichever variable has the positive coefficient
-> x^2 - y^2 = 1 is a hyperbola opening in x-direction
-> y^2 - x^2 = 1 is a hyperbola opening in x-direction