Question

write an equation of the circle with center (-3, -2) and radius 9.

Explanation:

Step1: Recall the standard equation of a circle

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: Identify the values of \(h\), \(k\), and \(r\)

Given the center \((-3, -2)\), we have \(h = -3\) and \(k = -2\). The radius \(r = 9\).

Step3: Substitute the values into the standard equation

Substitute \(h = -3\), \(k = -2\), and \(r = 9\) into \((x - h)^2 + (y - k)^2 = r^2\).
We get \((x - (-3))^2 + (y - (-2))^2 = 9^2\).
Simplifying the left - hand side, \((x + 3)^2 + (y + 2)^2 = 81\).

Answer:

The equation of the circle is \((x + 3)^2+(y + 2)^2 = 81\)