Question

use the graph given to answer questions #15 - 17. (1 point each)

1. what are the coordinates of the circles center?

(​ ​)

1. what is the radius of the circle?

r =​ ​

1. given the circle, write the equation of the circle in standard form.
2. which of the following points is on a circle centered at (-3, 1) with a radius of 5 units? (1 point)

a (-7, 2)
b (-2, 5)
c (0, 4)
d (2, 1)

Explanation:

Step1: Identify center from graph

By observing the graph, the center of the circle is at the point (-3, 1).

Step2: Determine radius from graph

Count the units from the center to a point on the circle. The radius $r = 3$.

Step3: Write circle equation

The standard - form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. Substituting $h=-3$, $k = 1$, and $r = 3$ gives $(x+3)^2+(y - 1)^2=9$.

Step4: Check points for circle

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For a circle centered at $(-3,1)$ with radius $r = 5$, we check each point:

• For point A$(-7,2)$: $d=\sqrt{(-7 + 3)^2+(2 - 1)^2}=\sqrt{(-4)^2+1^2}=\sqrt{16 + 1}=\sqrt{17}

eq5$.

• For point B$(-2,5)$: $d=\sqrt{(-2+3)^2+(5 - 1)^2}=\sqrt{1^2+4^2}=\sqrt{1 + 16}=\sqrt{17}

eq5$.

• For point C$(0,4)$: $d=\sqrt{(0 + 3)^2+(4 - 1)^2}=\sqrt{3^2+3^2}=\sqrt{9 + 9}=\sqrt{18}

eq5$.

• For point D$(2,1)$: $d=\sqrt{(2+3)^2+(1 - 1)^2}=\sqrt{5^2+0^2}=5$.

Answer:

1. (-3, 1)
2. 3
3. $(x + 3)^2+(y - 1)^2=9$
4. D. (2, 1)