Question

write the equation in standard form for the circle with center (-7, 4) and radius 2.

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, \(h = -7\), \(k = 4\), and \(r = 2\). Substitute these into the formula: \((x - (-7))^2 + (y - 4)^2 = 2^2\).

Step3: Simplify the equation

Simplify \(x - (-7)\) to \(x + 7\) and \(2^2\) to \(4\). So the equation becomes \((x + 7)^2 + (y - 4)^2 = 4\).

Answer:

\((x + 7)^2 + (y - 4)^2 = 4\)