To find the radius of the circle given the equation [tex]\((x-7)^2 + (y-10)^2 = 4\)[/tex], we need to understand the components of the standard form of a circle's equation. The standard form is [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex], where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
Given the equation:
[tex]\[ (x-7)^2 + (y-10)^2 = 4 \][/tex]
we can directly compare this with the standard form. Here, we identify that:
- [tex]\(h = 7\)[/tex]
- [tex]\(k = 10\)[/tex]
- [tex]\(r^2 = 4\)[/tex]
From [tex]\(r^2 = 4\)[/tex], we solve for [tex]\(r\)[/tex] by taking the square root of both sides:
[tex]\[ r = \sqrt{4} \][/tex]
Thus, we get:
[tex]\[ r = 2 \][/tex]
So, the radius of the circle is 2 units.
