Question

what is the diameter of the circle (x + 4)^2 + y^2 = 49? 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 $(x + 4)^2+y^2 = 49$, we can rewrite it as $(x-(-4))^2+(y - 0)^2=7^2$. So, $r^2 = 49$, and $r=\sqrt{49}=7$.

Step2: Calculate the diameter

The diameter $d$ of a circle is related to the radius $r$ by the formula $d = 2r$. Since $r = 7$, then $d=2\times7 = 14$.

Answer:

14