Question

what is the diameter of the circle $(x+\frac{26}{3})^2 + y^2 = 36$? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius. Given the equation $(x+\frac{26}{3})^2 + y^2=36$, we can rewrite it as $(x-(-\frac{26}{3}))^2+(y - 0)^2 = 36$.

Step2: Find the radius

Since $r^2 = 36$, then $r=\sqrt{36}=6$ (we take the positive value for the radius as it represents a distance).

Step3: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substituting $r = 6$ into the formula, we get $d=2\times6 = 12$.

Answer:

12