In the expression $(x-h)^2 + (y-k)^2$, what values of $h$ and $k$ give you $(3,-2)$? Which answer choices place those values correctly (watch the signs inside the parentheses)?

Once you have the correct center in the equation, plug in the coordinates of the point $(7,2)$ to find $r^2$. What value do you get?

In Desmos, enter each option on a separate line exactly as written, for example: (x-3)^2+(y+2)^2=32. You should see up to four circles on the graph.

Add two points: type (3,-2) and (7,2) on separate lines so their locations appear clearly on the graph.

Look at which circle has its center at the point (3,-2) (it should be exactly in the middle of the circle) and also passes through the point (7,2). The equation corresponding to that circle is the correct choice.

The equation of a circle with center $(h,k)$ and radius $r$ in the $xy$-plane is

Our job is to match this form using the given center and point on the circle.

The center is $(3,-2)$, so $h=3$ and $k=-2$.

Substitute these into the standard form:

which simplifies to

Any correct answer must have $(x-3)^2$ and $(y+2)^2$ on the left side.

The circle passes through $(7,2)$, so this point must satisfy the equation.

Substitute $x=7$ and $y=2$ into $(x-3)^2 + (y+2)^2 = r^2$:

Now calculate each part to find $r^2$.

Compute the expression:

So $r^2 = 32$.

Substitute this back into the circle equation:

which is the equation of the circle.