Questions: Write the standard form of the equation of the circle described below. Center (-3,6), r=4

Solution Steps

To write the standard form of the equation of a circle, we use the formula \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center \((-3, 6)\) and radius \(4\), we can substitute these values into the formula.

The center of the circle is given as \((-3, 6)\) and the radius is \(4\).

Using the standard form of the equation of a circle, which is

\[ (x - h)^2 + (y - k)^2 = r^2 \]

we substitute \(h = -3\), \(k = 6\), and \(r = 4\):

\[ (x - (-3))^2 + (y - 6)^2 = 4^2 \]

This simplifies to:

\[ (x + 3)^2 + (y - 6)^2 = 16 \]

Final Answer