Write the equation of a circle with center (4, -5) and radius = square root of 13

Hello!The answer is:The equation of the given circle is: [tex](x-4)^{2}+(y+5)^{2}=13[/tex]Why?The equation of a circle is given by the following equation:[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]We are given the center point (4,-5) and the radius.So,Where:[tex]h=x=4\\k=y=-5\\r=\sqrt{13}[/tex]Then, substituting into the circle equation, we have:[tex](x-4)^{2} +(y-(-5))^{2}=(\sqrt{13})^{2}[/tex][tex](x-4)^{2} +(y-(-5))^{2}=(\sqrt{13})^{2}[/tex]Hence, the simplified equation of the circle is:[tex](x-4)^{2}+(y+5)^{2}=13[/tex]Have a nice day!