Question

what is the diameter of the circle x² + (y + 15/2)² = 144? 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 $r$ is the radius. Given $x^{2}+(y+\frac{15}{2})^{2}=144$, we can see that $r^{2}=144$.

Step2: Find the radius

Take the square - root of both sides of $r^{2}=144$. Since $r>0$, we have $r = \sqrt{144}=12$.

Step3: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substitute $r = 12$ into the formula, we get $d=2\times12 = 24$.

Answer:

24