Question

what is the diameter of the circle $x^{2}+(y - \frac{33}{4})^{2}=16$? 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 $r$ is the radius. Given $x^{2}+(y-\frac{33}{4})^{2}=16$, we can compare it with the standard - form. Here, $r^{2}=16$.

Step2: Calculate the radius

Since $r^{2}=16$, taking the square - root of both sides, we get $r = 4$ (we consider the positive value of $r$ because the radius is a non - negative quantity).

Step3: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substituting $r = 4$ into the formula, we have $d=2\times4=8$.

Answer:

8