25x^(2)+9y^9(2)+150x-36y+260=0

Question

find the vertices,foci,center,and graph the ellipse.Could you show steps in between.

 

Answer 1

25x² + 150x + 9y² -36y = -260

25 (x² + 6x) + 9 (y² - 4y) = -260

25 [(x + 3)² - 9] + 9 [(y - 2)² - 4] = -260

25 * (x + 3)² - 25(9) + 9*(y - 2)² -9(4) = -260

25(x + 3)² + 9(y - 2)² = -260 + 25(9) + 9(4)

25(x + 3)² + 9(y - 2)² = -260 + 225 + 36

25(x + 3)² + 9(y - 2)² = 1

(25 * 9) [ ((x + 3)² / 9) + ((y - 2)²/25)] = (25 * 9)

(x + 3)² / 9 + (y - 2)² / 25 = 225

(1/225) * [(x + 3)² / 9 + (y - 2)² / 25] = 225/225

(x + 3)² / 2025 + (y - 2)² / 5625 = 1

figure out the rest