Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.

9514 1404 393

Step-by-step explanation:

The "center-radius" form is ...

  (x -h)² +(y -k)² = r² . . . . . . . circle with center (h, k) and radius r

The graphed circle has its center at (-5, 3) and a radius of 5. Putting these numbers into the above form gives the equation ...

  (x +5)² +(y -3)² = 25 . . . . center-radius form

Expanding the parentheses, we get ...

  x² +10x +25 +y² -6y +9 = 25

Subtracting 25, and putting in general form, the equation becomes ...

  x² +y² +10x -6y +9 = 0 . . . . general form

Additional comment

General form is f(x, y) = 0, where the terms of f(x, y) are lexicographical order and decreasing degree.