Questions: Write the equation of the circle centered at (1,-7) with radius 6.

Solution Steps

To write the equation of a circle, we use the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center \((1, -7)\) and radius \(6\), we can substitute these values into the equation.

The standard form of the equation of a circle is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((h, k)\) is the center of the circle and \(r\) is the radius.

Given the center \((1, -7)\) and radius \(6\), we substitute these values into the standard form: \[ (x - 1)^2 + (y - (-7))^2 = 6^2 \]

Simplify the equation by calculating the square of the radius: \[ (x - 1)^2 + (y + 7)^2 = 36 \]

Final Answer