state whether the eqaution 9x^2-25y^2+36z^2=1 is a:
1. A hyperboloid of two sheets
2. A hyperboloid of one sheet
3. An ellipsoid
4. None of these

Question

state whether the eqaution 9x^2-25y^2+36z^2=1 is a:
1. A hyperboloid of two sheets 
2. A hyperboloid of one sheet 
3. An ellipsoid 
4. None of these

turingtest · Answer

it seems to me to be a hyperboloid of one sheet

turingtest · Answer

http://tutorial.math.lamar.edu/Classes/CalcIII/QuadricSurfaces.aspx

turingtest · Answer

if all the coefficients were positive it would be an ellipsiod
if it had two negative coefficients it would be a hyperboloid of two sheets
with one negative coefficient, all equal to 1, it is a hyperboloid of one sheet
(that opens along the y-axis)

anonymous · Answer

what about z^2=(x/5)^2-(y/5)^2
1. A hyperbolic paraboloid 
2. An elliptic paraboloid 
3. An elliptic cone 
4. None of these

turingtest · Answer

can't you tell from the link I gave you?
which one has a variable equal to two other variables with a minus between them?

anonymous · Answer

a hyperbolic paraboloid but it says that it is incorrect

turingtest · Answer

the z is squared so it is not a hyperbolic paraboloid....

turingtest · Answer

if the z were to the first is would be.

turingtest · Answer

it*

anonymous · Answer

so then what is it

turingtest · Answer

read the list slowly; never mind the value of the coefficients, just their signs

turingtest · Answer

it's not too far down the list http://tutorial.math.lamar.edu/Classes/CalcIII/QuadricSurfaces.aspx which one has all variables squared, no minus signs, and is not equal to one?

anonymous · Answer

a cone

turingtest · Answer

yes (a circular cone at that)

anonymous · Answer

thank you

turingtest · Answer

welcome!

turingtest · Answer

oh wait your has a minus

anonymous · Answer

it was correct and i understand why

turingtest · Answer

oh yeah? I thought I messed up actually :S