25x^2+9y^2+72y-81=0. Find the standard form of the equation by completing the square. Then identify and graph each conic.

25x² + 9y² + 72y - 81 = 0

25x² + 9y² + 72y - 81 + 81 = 0 + 81

25x² + 9y² + 72y = 81

25x² + 9 (y² + 8y + 16) = 81 + 9 (16)

25x² + 9 (y² + 4y + 4y + 16) = 81 + 144

25x² + 9 (y (y) + 4 (y) + 4 (y) + 4 (4)) = 225

25x² + 9 (y (y + 4) + 4 (y + 4)) = 225

25x² + 9 (y + 4) (y + 4) = 225

25x² + 9 (y + 4) ² = 225

225 225 225

x² + 9 (y + 4) ² = 1

25 25

The conic section is an ellipse.