Question

14.8.2 test (cst): conic sections
this circle is centered at the point (2, 6), and the length of its radius is 4. what is the equation of the circle?
a. (x² - 2)+(y² - 6)=4²
b. (x - 2)²+(y - 6)²=16
c. (x + 2)²+(y + 6)²=4
d. (x - 6)²+(y - 2)²=16

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify values of \(h\), \(k\), and \(r\)

Given that the center is \((2,6)\), so \(h = 2\), \(k = 6\), and the radius \(r = 4\).

Step3: Substitute values into the formula

Substitute \(h = 2\), \(k = 6\), and \(r = 4\) into \((x - h)^2+(y - k)^2=r^2\), we get \((x - 2)^2+(y - 6)^2=4^2=16\).

Answer:

B. \((x - 2)^2+(y - 6)^2=16\)