Question

given a circle with center (2, - 6) and radius 1, (a) write an equation of the circle in standard form. (b) graph the circle.

Explanation:

Step1: Recall circle - standard - form formula

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

Step2: Identify values of $h$, $k$, and $r$

Given that the center is $(2,-6)$ and the radius $r = 1$, so $h = 2$, $k=-6$, and $r = 1$.

Step3: Substitute values into the formula

Substitute $h = 2$, $k=-6$, and $r = 1$ into $(x - h)^2+(y - k)^2=r^2$, we get $(x - 2)^2+(y+6)^2=1$.

For part (b), to graph the circle:

1. Locate the center of the circle at the point $(2,-6)$ on the coordinate plane.
2. Since the radius $r = 1$, use a compass with a radius of 1 unit and place the point of the compass at the center $(2,-6)$ and draw the circle.

Answer:

(a) $(x - 2)^2+(y + 6)^2=1$
(b) Locate the center at $(2,-6)$ and draw a circle with radius 1.