In Example 5, change the + before 8y to −.

Data from Example 5

Find the center and radius of the circle. x² + y² − 6x + 8y − 24 = 0

We can find this information if we write the given equation in standard form. [To do so, we must complete the square in the x-terms and also in the y-terms.] This is done by first writing the equation in the form (x² − 6x ) + (y² + 8y ) = 24

To complete the square of the x-terms, we take half of −6, which is −3, square it, and add the result, 9, to each side of the equation. In the same way, we complete the square of the y-terms by adding 16 to each side of the equation, which gives

Thus, the center is (3,−4), and the radius is 7 (see Fig. 21.36).

197 167 (x - 6x + 9) + (y + 8y + 16) = 24 + 9 + 16 (x - 3) + (y + 4) = 49 (x - 3) + [y-(-4)] = 7 coordinates of center radius add to both sides