Question

write the standard form of the equation of the circle described below.
center (6, -3), r = 9

the standard form of the equation of the circle is
(type an equation. simplify your answer.)

Explanation:

Step1: Recall the standard circle equation

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: Substitute the given values

Here, the center is \((6, -3)\), so \(h = 6\) and \(k = -3\), and the radius \(r = 9\). Substituting these into the formula, we get \((x - 6)^2 + (y - (-3))^2 = 9^2\).

Step3: Simplify the equation

Simplify \(y - (-3)\) to \(y + 3\) and \(9^2\) to \(81\). So the equation becomes \((x - 6)^2 + (y + 3)^2 = 81\).

Answer:

\((x - 6)^2 + (y + 3)^2 = 81\)