Answer :
I don't know what the answer to number 1 is.
2. Center
25x² + 4y² - 50x - 24y - 39 = 0
25x² + 4y² - 50x - 24y = 39
25x² - 50x + 4y² - 24y = 39
25(x² - 2x) + 4(y² - 6y) = 39
25(x² - 2x + 4) + 4(y² - 6y + 9) = 39 + 25(4) + 4(9)
25(x² - 2x + 4) + 4(y² - 6y + 9) = 39 + 100 + 36
25(x² - 2x + 4) + 4(y² - 6y + 9) = 175
25(x - 2)² + 4(y - 3)² = 175
175 175 175
(x - 2)² + 4(y - 3)² = 1
7 17
2. Center
25x² + 4y² - 50x - 24y - 39 = 0
25x² + 4y² - 50x - 24y = 39
25x² - 50x + 4y² - 24y = 39
25(x² - 2x) + 4(y² - 6y) = 39
25(x² - 2x + 4) + 4(y² - 6y + 9) = 39 + 25(4) + 4(9)
25(x² - 2x + 4) + 4(y² - 6y + 9) = 39 + 100 + 36
25(x² - 2x + 4) + 4(y² - 6y + 9) = 175
25(x - 2)² + 4(y - 3)² = 175
175 175 175
(x - 2)² + 4(y - 3)² = 1
7 17