Question

determine the equation of the circle graphed below.

Explanation:

Step1: Identify circle center

The center \((h,k)\) is at \((0,0)\) (intersection of axes).

Step2: Calculate radius length

Count units from center to rightmost point: \(r = 6\).

Step3: Plug into circle equation

Use standard form \((x-h)^2+(y-k)^2=r^2\).
$$(x-0)^2+(y-0)^2=6^2$$

Step4: Simplify the equation

$$x^2+y^2=36$$

Answer:

$\boldsymbol{x^2 + y^2 = 36}$