Question
Find standard equation of a circle with a center at $ \color{blue}{C = \left( 0 , 8 \right)} $ and radius $ \color{blue}{ 2 }$
Answer
The circle equation is:
$$ \color{blue}{ x^2 + \left( y - 8 \right)^2 = 4 }$$Explanation
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 = 0 } $, $ \color{red}{k = 8 }$ and $ r = 2 $, so after substituting into above formula we have:
$$ \begin{aligned} \left(x - 0 \right)^2 + \left(y - 8 \right)^2 &= 2^2 \\ x^2 + \left( y - 8 \right)^2 &= 4 \end{aligned} $$This page was created using
Circle equation Calculator