Problem

Write the standard form of the equation of the circle described below.
Center $(-8,3), r=3$

Answer

Expert–verified
Hide Steps
Answer

The standard form of the equation of the circle is \(\boxed{(x + 8)^2 + (y - 3)^2 = 9}\).

Steps

Step 1 :The standard form of the equation of a circle is given by \((x-a)^2 + (y-b)^2 = r^2\), where \((a, b)\) is the center of the circle and \(r\) is the radius.

Step 2 :In this case, the center of the circle is \((-8, 3)\) and the radius is \(3\).

Step 3 :We substitute these values into the standard form to get the equation of the circle.

Step 4 :The equation is \((x - (-8))^2 + (y - (3))^2 = 3^2\).

Step 5 :The standard form of the equation of the circle is \(\boxed{(x + 8)^2 + (y - 3)^2 = 9}\).

link_gpt