Question

This circle is centered at the point (4,5), and the length of its radius is 3. What is the equation of the circle?

O A. (x - 5)² + (x-4)² = 9
O B. (x + 4)2 + (y + 5)2 = 3
O c. (x-4)² + (x - 5)2 = 9
O D. (x²-4) + (7-5) = 32

Answer 1

`\textbf{The equation of the circle is: $ {(x-4)}^2 + {(y-5)}^2 = 9 $.}\\`

Explanation:

`\textup{The equation of a circle is given by:}\\$$c = \sqrt{{(x-h)}^2 + {(y-k)}^2} = r^2$$\\\textit{where $(h,k)$ represents the centre of the circle and $r$ the radius.}\\\textup{Given the centre of the circle is $(4,5)$ and radius is $3$.}\\$ \therefore $ We have $$c = \sqrt{{(x-4)}^2 + {(y-5)}^2} = 3^2$$$\implies {(x-4)}^2 + {(y-5)}^2 = 9$`