Question

given a circle where the center is (-8, -2) and another point on the circle is (-5, -6). (a) write an equation of the circle in standard form. (b) graph the circle. part: 0 / 4 part 1 of 4 the select of the circle is the distance between a point on the circle and the center.

Explanation:

Step1: Identify radius definition

The distance between circle center and its point is the radius.

Step2: Calculate radius length

Use distance formula: $r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Substitute $(-8,-2)$ and $(-5,-6)$:
$r = \sqrt{(-5-(-8))^2+(-6-(-2))^2} = \sqrt{(3)^2+(-4)^2} = \sqrt{9+16} = \sqrt{25} = 5$

Step3: Find radius squared

$r^2 = 5^2 = 25$

Step4: Write standard circle equation

Standard form: $(x-h)^2+(y-k)^2=r^2$, substitute $(h,k)=(-8,-2)$ and $r^2=25$:
$(x+8)^2+(y+2)^2=25$

Answer:

Part 1 of 4:

The radius of the circle is the distance between a point on the circle and the center.

Part (a):

$(x+8)^2+(y+2)^2=25$

Part (b):

To graph the circle:

1. Plot the center point $(-8, -2)$ on a coordinate plane.
2. Using a compass or by marking points 5 units away from the center in all directions (up, down, left, right, and diagonally), draw a smooth, closed curve connecting these points to form the circle.