Question

what is the diameter of the circle (x + 8)^2 + y^2 = 25? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle - equation form

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 $(x + 8)^2+y^2 = 25$, we can rewrite it as $(x-(-8))^2+(y - 0)^2=5^2$. So, the radius $r = 5$.

Step2: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substituting $r = 5$ into the formula, we get $d=2\times5$.

Answer:

10