Question

what is the center of the circle $(x - \frac{3}{2})^2+(y + \frac{17}{2})^2 = 65? simplify any fractions.

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle.

Step2: Identify the center - coordinates

For the given circle equation $(x-\frac{3}{2})^2+(y+\frac{17}{2})^2 = 65$, we can rewrite $y+\frac{17}{2}$ as $y-(-\frac{17}{2})$.
Comparing with the standard form, $h=\frac{3}{2}$ and $k =-\frac{17}{2}$.

Answer:

$(\frac{3}{2},-\frac{17}{2})$