Question

question 22
find the equation in standard form of the circle graphed below.
question help: written example

Explanation:

Step1: Identify center coordinates

The center of the circle is at $(1, - 1)$.

Step2: Determine radius

The distance from the center $(1,-1)$ to a point on the circle like $(3,-1)$ is $r=\vert3 - 1\vert=2$.

Step3: Write standard - form equation

The standard - form equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. Substituting $h = 1$, $k=-1$, and $r = 2$ gives $(x - 1)^2+(y + 1)^2=4$.

Answer:

$(x - 1)^2+(y + 1)^2=4$