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

Answer:

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

Step-by-step explanation:

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