Question

1. find the coordinates of the center and the measure of the radius for a circle whose equation is $(x - 3)^{2}+(y - 7)^{2}=2$.

center $=(-3,-7)$, radius $=4$
center $=(3,7)$, radius $=\sqrt{2}$
center $=(3,7)$, radius $=1$
center $=(-3,-7)$, radius $=1$

Explanation:

Step1: Recall circle standard form

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

Step2: Identify center coordinates

Compare $(x-3)^2 + (y-7)^2 = 2$ with the standard form: $h=3$, $k=7$. So center is $(3,7)$.

Step3: Calculate radius

The right-hand side is $r^2 = 2$, so $r = \sqrt{2}$.

Answer:

center = (3,7), radius = $\sqrt{2}$