Question

select the correct answer.
which equation represents a circle with center t(5,-1) and a radius of 16 units?
a. (x - 5)^2 + (y + 1)^2 = 16
b. (x - 5)^2 + (y + 1)^2 = 256
c. (x + 5)^2 + (y - 1)^2 = 16
d. (x + 5)^2 + (y - 1)^2 = 256

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: Identify the center and radius from the given information

Given center \(T(5,-1)\), so \(h = 5\), \(k=-1\). Given radius \(r = 16\).

Step3: Substitute \(h\), \(k\), and \(r\) into the standard form

Substitute \(h = 5\), \(k=-1\), \(r = 16\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 5)^2+(y-(-1))^2=16^2\), which simplifies to \((x - 5)^2+(y + 1)^2=256\).

Answer:

B. \((x - 5)^2+(y + 1)^2=256\)