The expression $(x-2)^2 + (y-3)^2$ resembles the general form of the equation of a circle. However, it seems incomplete because it does not equate to a value (typically representing $r^2$, where $r$ is the radius of the circle).

To complete the equation, you would set it equal to $r^2$, where $r$ is the radius of the circle. For example:

$(x-2)^2 + (y-3)^2 = r^2$

This equation represents a circle with:

• Center at $(2, 3)$
• Radius $r$

If you have a specific radius in mind, you can substitute that value for $r^2$. For example, if the radius is 5, the equation would be:

$(x-2)^2 + (y-3)^2 = 25$

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you find the radius given the equation $(x-h)^2 + (y-k)^2 = r^2$?
2. What is the distance formula between two points, and how is it related to the equation of a circle?
3. How would you rewrite $(x-2)^2 + (y-3)^2 = 16$ in expanded form?
4. What is the equation of a circle passing through the origin and centered at $(2, 3)$?
5. How do you determine whether a point lies inside, on, or outside the circle given its equation?

Tip: When dealing with circles, remember that the squared terms of $x$ and $y$ indicate the geometric relationship between the coordinates and the circle's center.