Answer:
[tex](x-5)^2+(y+2)^2=9[/tex]
Step-by-step explanation:
The information that we know about the circle is the following:
center of the circle: (5, -2)
radius: [tex]r=3[/tex]
We use the general form for the equation of a circle whose center is at the point [tex](h,k)[/tex] :
[tex](x-h)^2+(y-k)^2=r^2[/tex]
In this case since the center of our circle is at (5, -2), we conclude that:
[tex]h=5[/tex]
and
[tex]k=-2[/tex]
so we substitute this values, along with the value for the radius:
[tex](x-5)^2+(y-(-2))^2=3^2[/tex]
simplifying the expression we get the equation of the circle:
[tex](x-5)^2+(y+2)^2=9[/tex]
