Question

Describe and sketch the surface of equation \({\rm{xy = 1}}\)

Short answer

The surface of equation \({\rm{xy = 1}}\) is described and sketched.

Step-by-step solution

Represent the Surface of Equations

The equation\({\rm{xy = 1}}\)represents\(\left\{ {(x,y,z)\mid z = 1 - {y^2}} \right\}\)and does not involve\(z\)-coordinates. Hence, set the\(x\)-plane equation as\(x = k\), where\(k\)is a constant.

Therefore, the resultant curve of equation \({\rm{xy = 1}}\) forms a hyperbolic cylinder with a duplicate of the same hyperbola in plane \(z = k\). The rulings in the representation of \(xy = I\) are parallel to the \(z\)-axis.

The sketch of equation \(xy = 1\) is shown below.

Thus, the surface of equation \(xy = 1\) is described and sketched.