Question

a circle in the xy - plane has a diameter with endpoints (2, 4) and (2, 14). an equation of this circle is ((x - 2)^2+(y - 9)^2 = r^2), where (r) is a positive constant. what is the value of (r)?

Explanation:

Step1: Find diameter length

The distance between endpoints $(2,4)$ and $(2,14)$ is $|14 - 4| = 10$.

Step2: Calculate radius $r$

Radius is half the diameter: $r = \frac{10}{2} = 5$.

Answer:

$5$