Answer:
[tex](x-2)^2+(y-4)^2=25[/tex]Explanation:
Given a circle with center N(2,4) and radius MN where M(-2,1).
First, we find the length of the radius using the distance formula.
[tex]\begin{gathered} MN=\sqrt[]{(-2-2_{})^2+(1-4)^2} \\ =\sqrt[]{(4_{})^2+(-3)^2} \\ =\sqrt[]{25} \\ r=5\text{ units} \end{gathered}[/tex]The equation of a circle is of the form:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k)=N(2,4), r=5
Therefore, the equation is:
[tex]\begin{gathered} (x-2)^2+(y-4)^2=5^2 \\ (x-2)^2+(y-4)^2=25 \end{gathered}[/tex]