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
<u>25x²</u> + <u>9(y + 4)²</u> = <u>225</u>
225 225 225
<u> x²</u> + <u>9(y + 4)²</u> = 1
25 25
The conic section is an ellipse.
Answer: 20790
Step-by-step explanation:
