Question

(x + 55)^2+(y - 11.5)^2 = 121
a circle in the xy - plane has the equation shown. what is the length of the diameter of the circle?

Explanation:

Step1: Recall the standard - form of a circle equation

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 $(x + 55)^2+(y - 11.5)^2 = 121$, we can rewrite it as $(x-(-55))^2+(y - 11.5)^2=11^2$.

Step2: Identify the radius

Comparing with the standard - form, we have $r^2 = 121$, so $r=\sqrt{121}=11$.

Step3: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substituting $r = 11$ into the formula, we get $d=2\times11 = 22$.

Answer:

22