Question

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

Answer 1

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.