Question

given a circle with center (1, -3) and radius 1, (a) write an equation of the circle in standard form. (b) graph the circle.

Explanation:

Step1: Recall the standard - form equation of a circle

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

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

Given $h = 1$, $k=-3$, and $r = 1$.

Step3: Substitute the values into the standard - form equation

Substituting into $(x - h)^2+(y - k)^2=r^2$, we get $(x - 1)^2+(y-(-3))^2=1^2$, which simplifies to $(x - 1)^2+(y + 3)^2=1$.

Answer:

(a) $(x - 1)^2+(y + 3)^2=1$
(b) To graph the circle:

1. Locate the center $(1,-3)$ on the coordinate - plane.
2. From the center, move 1 unit in all directions (up, down, left, and right) to mark points on the circle. Then, sketch the circle passing through these points.