Step 1

Given:

The pair of equations:

\(\displaystyle{x}^{{2}}+{y}^{{2}}={4},{z}={y}\)

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

Step 2

The equation \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}\) gives the circle in the X-Y plane with centre of the circle is the origin(0, 0) with radius of the circle is r=2 and the equation z=y is the plane

The pair of both the equation is the intersection of the plane z=y and circle \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}\) which satisfy the two circle \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}{\quad\text{and}\quad}{x}^{{2}}+{z}^{{2}}={4}\)

Given:

The pair of equations:

\(\displaystyle{x}^{{2}}+{y}^{{2}}={4},{z}={y}\)

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

Step 2

The equation \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}\) gives the circle in the X-Y plane with centre of the circle is the origin(0, 0) with radius of the circle is r=2 and the equation z=y is the plane

The pair of both the equation is the intersection of the plane z=y and circle \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}\) which satisfy the two circle \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}{\quad\text{and}\quad}{x}^{{2}}+{z}^{{2}}={4}\)