Step 1: Find circle radius

To find a radius of a circle we will compute the distance between points $ C $ and $ P $. Distance can be computed by using formula:

$$ r = \sqrt{ \left(C_x - P_x\right)^2 + \left(C_y - P_y\right)^2 } $$

In this example $ C_x = -8 $ , $ C_y = -5 $, $ P_x = 1 $ , $ P_y = -5 $, and after substituting these values into the formula we get $ r = 9 $ ( to see complete explanation on how to find distance click here )

Step 2: The equation of a circle with center at $(\color{blue}{h} , \color{red}{k})$ and a radius of $ r $ is:

$$ (x - \color{blue}{h} )^2 + (y - \color{red}{k})^2 = r^2 $$

In this example $ \color{blue}{h = -8 } $, $ \color{red}{k = -5 }$ and $ r = 9 $, so after substituting into above formula we have:

$$ \begin{aligned} \left(x - \left( -8 \right) \right)^2 + \left(y - \left( -5 \right)\right)^2 &= 9^2 \\ \left( x + 8 \right)^2 + \left( y + 5 \right)^2 &= 81 \end{aligned} $$

Circle equation Calculator