Question

The equation of a circle is given below. Identify the radius and center. Then graph the circle.(x-4)^2+(y-1)^2=9Radius:Center:

Answer 1

Radius: 3

center = (4, 1)

Explanation:

`\begin{gathered} \text{Given the equation of a circle to be } \\ (x-4)^2+(y-1)^2\text{ =9} \\ \text{The standard form for the equation of a circle is} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{let (a, b) be the coordinate and r = radius} \\ -a\text{ = -4} \\ a\text{ = 4} \\ -b\text{ = -1} \\ b\text{ = 1} \\ r^2\text{ = 9} \\ \text{Take the square roots of both sides} \\ r\text{ = }\sqrt[]{9} \\ r\text{ = 3} \\ \text{Therefore, the center of the circle is (4, 1) and radius = 3} \end{gathered}`