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The region in space represented by the equation x = 2 is a plane perpendicular to the x-axis. It contains all points whose x-coordinate is 2. The y- and z-coordinates can be anything. We can plot this parametrically by setting the setting the x-coordinate to 2, and letting the y- and z-coordinates vary over arbitrary intervals.

> plot3d([2,s,t],s=-5..5,t=-5..5,axes=normal,labels=["x","y","z"]);

Note that the plane x = 2 divides space into two disjoint regions. One region consists of all points with x-coordinates greater than 2, and this region is then described by the inequality x > 2. The region on the opposite side of the plane x = 2 contains all points with x-coordinates less than 2, and hence is described by the inequality x < 2.

Similarly, the equation y = 5 is a plane perpendicular to the y-axis containing all points whose y-coordinate is 5. This region can be plotted parametrically by setting the y-coordinate to 5, and letting the x- and z-coordinates vary over arbitrary intervals. The two regions x = 2 and y = 5 can be plotted on the same set of axes as follows.

> plot3d({[2,s,t],[s,5,t]},s=-5..5,t=-5..5,axes=normal, labels=["x","y","z"]);

Note that the plane x = 2 and the plane x = 5 intersect in a straight line. All points on this line have x-coordinate 2 and y-coordinate 5. Now let us add a third plane z = -3.

> plot3d({[2,s,t],[s,5,t],[s,t,-3]},s=-5..5,t=-5..5,axes=normal,labels=["x","y","z"]);

These three planes have exactly one point in common. This point is the point whose coordinates are x = 2, y = 5, and z = -3.

A sphere with center at the origin and radius 5, can be drawn parametrically as follows:

> plot3d([5*cos(2*Pi*s)*sin(Pi*t),5*sin(2*Pi*s)*sin(Pi*t),5*cos(Pi*t)],s=0..1,t=0..1,axes=boxed,scaling=constrained);

To put the center of the sphere at [2,5,-3], just add these coordinates to the above representation. We also add portions of the coordinate planes to help view the position of the sphere.

> plot3d({[2+5*cos(2*Pi*s)*sin(Pi*t),5+5*sin(2*Pi*s)*sin(Pi*t),-3+5*cos(Pi*t)],[0,-2*(1-s)+10*s,-9*(1-t)+3*t],[-2*(1-s)+7*s,0,-9*(1-t)+3*t],[-2*(1-s)+7*s,-2*(1-t)+10*t,0]},s=0..1,t=0..1,axes=boxed,scaling=constrained);

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