Given,
The coordinates of the point on the circle is (-4, -2).
The coordinates of the center of the circle is (-8, -10).
Reuired
The length of the center of the circle.
By using the distance formula, the radius of the circle can be calculated.
The distance formula is,

Substituting the value of the coordinates of the points,
![\begin{gathered} Distance=√((-10-(-2))^2+(-8-(-4))^2) \\ =√((-10+2)^2+(-8+4)^2) \\ =√((-8)^2+(-4)^2) \\ =√(64+16) \\ =√(80) \\ =√(4*4*5) \\ =4\sqrt[]{5} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/249h9xyw7lvd3xd91nr6xj7j45cfoges24.png)
Hence,