Hello there. To solve this question, we have to remember some properties about equations of circles.
Given the following equation:
[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]
It is called the equation of a circle with center at
[tex](x_0,\,y_0)[/tex]
And radius R.
In the question, it gives us two equations that we might describe the shape of the equation, considering its key features (center, foci, asymptotes, semi-major and semi-minor axes, if applicable).
We have that
[tex](x+4)^2+(y-2)^2=16[/tex]
Is the equation of a circle with center at (-4, 2) and radius equal to
[tex]R=\sqrt{16}=4[/tex]
For the other equation
[tex](x-2)^2+(y-5)^2=64[/tex]
Is also the equation of a circle, with center at (2, 5) and radius equal to
[tex]R=\sqrt{64}=8[/tex]
