The common points to both the graphs is required.
The number of points common to both graphs is A. 1
The first equation is
[tex]x^2+y^2=4[/tex]
This is a circle with its center at the origin and radius of 2 units.
The second equation is
[tex]y=2[/tex]
This is a horizontal line passing through [tex]y=2[/tex].
Let us substitute the y value in the first equation
[tex]x^2+2^2=4\\\Rightarrow x^2=0\\\Rightarrow x=0[/tex]
The intersection point is [tex](0,2)[/tex].
There is only one common point.
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