Question

if (x - h)=4 and (y - k)=3, what is the radius of the circle above?
a. 1
b. 25
c. 7
d. 5

Explanation:

Step1: Apply Pythagorean theorem

The distance from the center \((h,k)\) to a point \((x,y)\) on the circle (radius \(r\)) forms a right - triangle. By the Pythagorean theorem \(r^{2}=(x - h)^{2}+(y - k)^{2}\). Given \((x - h)=4\) and \((y - k)=3\), then \(r^{2}=4^{2}+3^{2}\).

Step2: Calculate \(r^{2}\)

\(r^{2}=16 + 9=25\).

Step3: Find \(r\)

Take the square - root of both sides. Since \(r>0\), \(r=\sqrt{25}=5\).

Answer:

D. 5