Question

a circle is centered at (7, 8) and has a radius of 11. which of the following is the equation for this circle? (x - 7)^2 + (y - 8)^2 = 121 (x - 7)^2 + (y - 8)^2 = 11 (x + 7)^2 + (y + 8)^2 = 121 (x + 7)^2 + (y + 8)^2 = 11

Explanation:

Step1: Recall circle - equation formula

The standard form of the 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 \((7,8)\), so \(h = 7\), \(k = 8\), and the radius \(r = 11\).

Step3: Substitute values into the formula

Substitute \(h = 7\), \(k = 8\), and \(r = 11\) into \((x - h)^2+(y - k)^2=r^2\), we get \((x - 7)^2+(y - 8)^2=11^2=121\).

Answer:

\((x - 7)^2+(y - 8)^2 = 121\)