# Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. x^2 + y^2 = 4, z = y

Question
Equations
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$\displaystyle{x}^{{2}}+{y}^{{2}}={4},{z}={y}$$

2020-12-25
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 $$\displaystyle{x}^{{2}}+{y}^{{2}}={4}{\quad\text{and}\quad}{x}^{{2}}+{z}^{{2}}={4}$$

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