Answer:

r= 2 ; center: (1/3, -4/3)

Step-by-step explanation:

9x²+9y²-6x+24y=19

9x²-6x+9y²+24y=19

9(x²-2/3x + ___) + 9y²+24y=19 + ___

9(x²-2/3x+1/9) + 9y²+24y= 19+___

9(x²-2/3x+1/9) + 9y²+24y=19+9 × 1/9

9(x-1/3)²+9y²+24y=20

9(x-1/3)²+9(y²+8/7y+ ___)= 20 + ____

9(x-1/3)²+9(y²+8/7y+____)= 20 + ____

9(x-1/3)²+9(y²+8/7y+16/9)=20+____

9(x-1/3)²+9(y²+8/7y+16/9)=20+9 × 16/9

9(-1/3)²+9(y+4/3)²=36

(-1/3)²+(y+4/3)²=4

Step-by-step explanation:

9x² + 9y² - 6x + 24y =19

9x² - 6x + 9y²+ 24y = 19

3x² - 2x + 3y² + 8y =

19

3