To solve this, we are going to use the center-radius form of a circle equation: [tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
[tex](h,k)[/tex] is the center of the circle
[tex]r[/tex] is the radius of the circle
Since the center of our circle is [tex](4,5)[/tex], [tex]h=4[/tex] and [tex]k=5[/tex]. We also now that its radius is 7, so [tex]r=7[/tex]. Lets replace those values in our equation:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
[tex](x-4)^{2}+(y-5)^{2}=7^{2}[/tex]
We can conclude that the equation of a circle with center at the point (4,5) and radius 7, is [tex](x-4)^{2}+(y-5)^{2}=7^{2}[/tex]
