Question

the circumference of the circle is about select choice units and its area is about select choice square units. p(3, - 2) q(-2,2)

Explanation:

Step1: Calculate the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the radius $r$ between the center $P(3,-2)$ and a point on the circle $Q(-2,2)$. Here $x_1 = 3,y_1=-2,x_2=-2,y_2 = 2$. Then $r=\sqrt{(-2 - 3)^2+(2+ 2)^2}=\sqrt{(-5)^2+4^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.4$.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substitute $r\approx6.4$ into it, $C=2\pi\times6.4\approx2\times3.14\times6.4 = 40.192\approx40.2$.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r\approx6.4$ into it, $A=\pi\times(6.4)^{2}\approx3.14\times40.96 = 128.6144\approx128.6$.

Answer:

The circumference is about $40.2$ units and its area is about $128.6$ square units.