Question

what is the equation of a circle with center (8, 6) and radius 5?
a. $(x - 8)^2+(y - 6)^2 = 5$
b. $(x + 8)^2+(y + 6)^2 = 25$
c. $(x - 8)^2+(y - 6)^2 = 25$
d. $(x + 8)^2+(y + 6)^2 = 5$

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Substitute the given values

Given center \((h,k)=(8,6)\) and radius \(r = 5\). Substitute into the formula: \((x - 8)^2+(y - 6)^2=5^2\).

Step3: Simplify

Since \(5^2=25\), the equation is \((x - 8)^2+(y - 6)^2=25\).

Answer:

C. \((x - 8)^2+(y - 6)^2=25\)