Answer:
[tex](x-4)^2+(y+2)^2=4[/tex]
Step-by-step explanation:
A circle is the set of all points on a plane at a given distance (radius) from a given point (center). The general equation of a circle with center [tex](h,k)[/tex] and radius [tex]r[/tex] is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Therefore, replacing the data provided into the previous equation:
[tex]Center=(4,-2)=(h,k)\\\\h=4\\\\k=-2\\\\Radius=2\\\\r=2[/tex]
[tex](x-(4))^2+(y-(-2))^2=(2)^2\\\\(x-4)^2+(y+2)^2=4[/tex]
So, the equation of a circle with a radius of 2 and its center at (4,-2) is:
[tex](x-4)^2+(y+2)^2=4[/tex]
I attach you the graph.
