Question

question 1, 2.4.9 part 1 of 3 find the center and radius of the circle. write the standard form of the equation. the center of the circle is (h,k)=□. (type an ordered pair.)

Explanation:

Step1: Identify center from graph

The center of the circle is given as the point \((-2,-1)\) on the graph. So, \((h,k)=(-2,-1)\).

Step2: Calculate the radius

The radius \(r\) is the distance between the center \((-2,-1)\) and the point \((0, - 1)\) on the circle. Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), here \(x_1=-2,y_1 = - 1,x_2=0,y_2=-1\). Then \(r=\sqrt{(0+2)^2+(-1 + 1)^2}=\sqrt{4+0}=2\).

Step3: Write the standard - form of the circle equation

The standard - form of a circle equation is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h=-2,k = - 1,r = 2\) into the equation, we get \((x + 2)^2+(y+1)^2=4\).

Answer:

The center of the circle is \((h,k)=(-2,-1)\), the radius \(r = 2\), and the standard - form of the equation is \((x + 2)^2+(y + 1)^2=4\)