Answer:
If the radius is really 5.2, then the standard equation of this circle is:
[tex](x-4)^2+(y+2)^2=27.04[/tex]
Now, if there was a typo in your question, and the radius is "5", then, the equation becomes:
[tex](x-4)^2+(y+2)^2=25[/tex]
Step-by-step explanation:
Recall that the standard equation for a circle of radius R, centered at [tex](x_0,y_0)[/tex], is given by:
[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]
Therefore in the case of a circle of radius R = 5.2, and centered at (4, -2), we have:
[tex](x-x_0)^2+(y-y_0)^2=R^2\\(x-4)^2+(y-(-2))^2=(5.2)^2\\(x-4)^2+(y+2)^2=27.04[/tex]
