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 the radius using diameter - length formula

The length of the diameter is the distance between the two given points $(2,4)$ and $(2,14)$. Since the $x$-coordinates are the same, the length of the diameter $d$ is the absolute - value of the difference in $y$-coordinates. So $d=\vert14 - 4\vert=10$.

Step2: Calculate the radius

The radius $r$ of a circle is half of the diameter. So $r=\frac{d}{2}$. Since $d = 10$, then $r=\frac{10}{2}=5$.

Answer:

$5$