Give a Geometric Descripstion of The Set of Points

Question

Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations:

 

x^2 + y^2 + z^2 = 25, y = -4.

 

 

Thank you in advance :)

Answer 1

If you had x² + y² = 25, you would recognize this as a circle in the xy plane with a radius of 5. y = -4 would simply be a line parallel to the x axis where y = -4 cutting through the circle.

In 3 dimensions, x² + y² + z² = 25 would represent a sphere with a radius of 5. y=-4 would represent the equation for a plane parallel to the x,z axis where in all cases y = -4. Therefore, you could think of this plane slicing through the sphere at y = -4.