Question

15 mark for review
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 length of the diameter

The diameter endpoints are \((2, 4)\) and \((2, 14)\). Since the \(x\)-coordinates are the same, the distance (length of diameter) is the difference in \(y\)-coordinates: \(14 - 4 = 10\).

Step2: Find the radius

The radius \(r\) is half of the diameter. So \(r=\frac{10}{2}=5\).

Answer:

\(5\)