Explanation
For the first question
We are asked to write the equation of the circle given that
[tex]\begin{gathered} center:(13,-13) \\ Radius:4 \end{gathered}[/tex]
The equation of a circle is of the form
[tex](x-a)^2+(y-b)^2=r^2[/tex]
In our case
[tex]\begin{gathered} a=13 \\ b=-13 \\ r=4 \end{gathered}[/tex]
Substituting the values
[tex](x-13)^2+(y+13)^2=4^2[/tex]
For the second question
Given that
[tex](18,-13)\text{ and \lparen4,-3\rparen}[/tex]
We will have to get the midpoints (center) first
[tex]\frac{18+4}{2},\frac{-13-3}{2}=\frac{22}{2},\frac{-16}{2}=(11,-8)[/tex]
Next, we will find the radius
Using the points (4,-3) and (11,-8)
[tex]undefined[/tex]
