Question

The circle below is centered at the point (8,4) and has a radius of length 4.

What is its equation?
O A. (x-4)2 + (y + 8)2 = 4
O B. (x-8)2 + (y-4)2 =
16
O C. (x-4)2 + (7-8)2 =
10
42
O D. (x+8)2 + (9-4)2 =
16
SUBMIT

Answer 1

`\textbf{The equation of the circle is: $ {(x-8)}^2 + {(y-4)}^2 = 16 $.}\\`

Explanation:

`\textup{The equation of a circle is given by:}\\$$c = \sqrt{{(x-h)}^2 + {(y-k)}^2} = r^2$$\\\textit{where $(h,k)$ represents the centre of the circle and $r$ the radius.}\\\textup{Given the centre of the circle is $(8,4)$ and radius is $4$.}$ \therefore $ We have $$c = \sqrt{{(x-8)}^2 + {(y-4)}^2} = 4^2$$$\implies {(x-8)}^2 + {(y-4)}^2 = 16$`