answer this, do me a favour (1 Viewer)

[fatmuscle]

Briefly explain why the equation Y=7 represent a line in 2D space in the XY plane, even though there is no X term in the formula. Then think about which of these formulas below represents the surface that is a cylinder, 2 units from the X axis, in 3D space. Make sketches of all the surfaces indicated.

x^2+y^2+z^2= 4

x^2+y^2=4

y^2+z^2= 4

x^2+z^2=4


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if you can do this, much appreciated

graphics are welcome.

 

[Grey Council]

hrm, this belongs in the extracurricular, me thinks

 

[CM_Tutor]

y = 7 represents a line in 2d space as, for any x value, y is 7. It might help to think that y = 7 can also be written as y = f(x), where f(x) = 7 for all x.

Originally posted by fatmuscle
x^2+y^2+z^2= 4

x^2+y^2=4

y^2+z^2= 4

x^2+z^2=4

The first graph is a sphere of radius 2.

The other 3 are all cylinders of radius 2, the first about the z axis, the second about the x axis and the third about the y axis.

For the first, the reason is that at any particular z value, the cross section is a circle of radius 2 in the x and y directions. Similarly for the others.

Hope this helps.

 

[McLake]

Moves ...

 

[Affinity]

y= 7 is same as
0x + 1y = 7

which has general solution (x,y) = (0,7) + k(1,0) for parameter k

which you can see is 1 dimensional, hence a line