Geometric Descriptions

Question

Give a Geometric description of the set of points in space whose coordinates satisfy the pair of equations or inequalities. 

 

1) z=x+1 , no restriction on y

 

2) x²+y²+z²=25, x=3

Answer 1

1)  A plane; 1 linear constraint in 3-space yields a plane

2.)  substituting x = 3 into x^2 +y^2+z^2 = 25 yields 9 + y^2 + z^2 = 25, or y^2 + z^2 = 16

x = 3; y^2 + z^2 = 16 is a circle centered at (3, 0, 0) with radius 4 that is parallel to the y-z plane.

Answer 2

The equation x²+y²+z²=25 is a three dimensional function that gives you a sphere with a center of (0,0,0) and a radius of 5. If x=3, upon plugging this known value, the values that satisfy both equations are x=3,y=0,z=4. Given that the y stays at 0 in both conditions that means that the center of the sphere stays on the x-y plane. 

 

Let me know if this is sufficient, or if you need more understanding.