Question

what is the diameter of the circle (x + 7)^2 + y^2 = 36? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle - equation form

The standard form of a circle's 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 $(x + 7)^2+y^2 = 36$, we can rewrite it as $(x-(-7))^2+(y - 0)^2=6^2$. So, the radius $r = 6$.

Step2: Calculate the diameter

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

Answer:

12