Question

give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations.

Answer 1

x=2 y=3

y=0 z=0

x^2+y^2=4 z= 0

Answer 2

What is it exactly asking me to do?

Answer 3

For the first problem, how would you describe (in 3D space) the set of all points (x,y,z) where x=2 and y=3?

Answer 4

It would be in the xy plane

Answer 5

Would it? If x=2 and y=3 are the only requirements, then couldn't z be anything?

Answer 6

It would be in the xy plane perpendicular to the z

Answer 7

Here's what the point (2,3,0) would look like, right?

Answer 8

Yes

Answer 9

And here's x=2, y=3, z=anything

Answer 10

So it would be in the xyz plane?

Answer 11

The xz plane

Answer 12

All three of the problems are in 3D space (not necessarily in a single "plane"). I think what they're looking for in the first one is:
"A line perpendicular to the xy-plane at x=2, y=3"

Answer 13

The line through (2,3,0) is parallel to the z-axis

Answer 14

@DDCamp why wouldn't it just be a line segment origin to point (2,3)

Answer 15

How did they get that

Answer 16

@Ashley1nOnly It is parallel to the z-axis, but the z-axis is perpendicular to the xy-plane. It's two ways of saying the same thing.

Answer 17

@triciaal The problem says "set of points in space whose coordinates satisfy the given pairs of equations." The points on the line segment you described don't satisfy the conditions that x=2 and y=3.

Answer 18

of course it does (2,3,0) (x,y,z)

Answer 19

The line through (2,3,0) is parallel to the z-axis

was the answer. How is it parallel to the z-axis, it looks perpendicular

Answer 20

So it in the xy plane and its parallel to the z axis

Answer 21

The next one is it on the x plane?

Answer 22

the last one a circle in the xy plane