Question

what is the equation of the circle shown in the graph? ()² + ()² = 6 9 12 36

Explanation:

Step1: Identify the center

The center of the circle is at (-6, 4). In the standard - form equation of a circle \((x - h)^2+(y - k)^2=r^2\), \(h=-6\) and \(k = 4\). So the left - hand side of the equation is \((x+6)^2+(y - 4)^2\).

Step2: Determine the radius

Count the distance from the center (-6, 4) to a point on the circle, say (0, 4). The distance \(r\) (radius) is 6. Then \(r^2=36\).

Answer:

\((x + 6)^2+(y - 4)^2=36\)