The problem asks for the radius of circle X, given the center of the circle as $(4, -1)$ and a point on the circle as $(9, -13)$.

To find the radius, we use the distance formula, which calculates the distance between two points on a coordinate plane:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where:

• $(x_1, y_1)$ is the center of the circle $(4, -1)$,
• $(x_2, y_2)$ is a point on the circle $(9, -13)$.

Now, substitute the coordinates into the formula:

$d = \sqrt{(9 - 4)^2 + (-13 - (-1))^2}$ $d = \sqrt{(5)^2 + (-12)^2}$ $d = \sqrt{25 + 144}$ $d = \sqrt{169}$ $d = 13$

Thus, the radius of the circle is 13 units.

Would you like further clarification on the steps, or do you have additional questions on this topic?

Here are some related questions you might find helpful:

1. How do you find the equation of a circle if the center and radius are known?
2. What are some applications of the distance formula in geometry?
3. How can you derive the distance formula from the Pythagorean Theorem?
4. What does the general equation of a circle look like?
5. How can the distance formula be extended to higher dimensions (3D)?

Tip: When using the distance formula, it's essential to square the differences between the corresponding coordinates, as this ensures the result is always positive.