Question

write the equation in standard form for the circle with center (-7, 6) and radius 12.

Explanation:

Step1: Recall circle standard form

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 center and radius

Here, \(h = -7\), \(k = 6\), and \(r = 12\). Substitute these into the formula: \((x - (-7))^2 + (y - 6)^2 = 12^2\).

Step3: Simplify the equation

Simplify \(x - (-7)\) to \(x + 7\) and \(12^2\) to \(144\). So the equation becomes \((x + 7)^2 + (y - 6)^2 = 144\).

Answer:

\((x + 7)^2 + (y - 6)^2 = 144\)