Final answer:
The radius of the circle with a center at (1,0) and a point on the circle at (-4,3) is √34.
Step-by-step explanation:
In order to find the radius of the circle, we need to understand the relationship between the coordinates of the center and a point on the circle. The distance between the center and any point on the circle is equal to the radius of the circle.
Given that the center of the circle is (1,0) and a point on the circle is (-4,3), we can use the distance formula to find the radius:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values into the formula:
Distance = √((-4 - 1)^2 + (3 - 0)^2) = √((-5)^2 + 3^2) = √(25 + 9) = √34
So, the radius of the circle is √34.