Question
Find the center and radius of the circle $ \left( x + 9 \right)^2 + \left( y - 8 \right)^2 = 400 $.
Answer
The center of the circle is at: $ C = \left(-9, 8\right) $.
The radius of the circle is $ r = 20 $.
Explanation
A circle with center at $ ( \color{red}{h}, \color{blue}{k}) $ and a radius of $ r $ has equation $ (x - \color{red}{h})^2 + (y - \color{blue}{k})^2 = r^2 $.
In this example our circle equation can be written as:
$$ \left( x - \left(\color{red}{ -9 } \right) \right)^2 + \left( y - \color{blue}{ 8 } \right)^2 = \left( 20 \right)^2 $$So, we have: $ \color{red}{h = -9 }$ , $ \color{blue}{ k = 8 }$ and $ r = 20 $.
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Circle equation Calculator