Question

write the equation in standard form for the circle with center (9, 0) and radius 6.

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

Given center \((9, 0)\), so \(h = 9\), \(k = 0\), and radius \(r = 6\). Substitute into the formula: \((x - 9)^2 + (y - 0)^2 = 6^2\).

Step3: Simplify the equation

Simplify \((y - 0)^2\) to \(y^2\) and \(6^2\) to \(36\), getting \((x - 9)^2 + y^2 = 36\).

Answer:

\((x - 9)^2 + y^2 = 36\)