Answer
a. $(4,5)$
b. $\sqrt 2$
c. $(x-4)^2+(y-5)^2=2$
Work Step by Step
a. Given the coordinates of the ends of a diameter: $(3,6)$ and $(5,4)$, we can find the center of the circle as $(\frac{5+3}{2},\frac{4+6}{2})$ or $(4,5)$
b. The radius is half of the diameter; we have $r=\frac{\sqrt {(5-3)^2+(4-6)^2}}{2}=\frac{\sqrt {4+4}}{2}=\sqrt 2$
c. Based on the above results, we can write the standard form of the circle’s equation as $(x-4)^2+(y-5)^2=2$
