Question

write each equation in standard form 9x^2 + 4y^2 - 54x + 24y +81 = 0

Answer 1

Can you identify what equation this is??

Answer 2

its a hyperbola

Answer 3

or do you mean something different

Answer 4

You know how to complete the squares. You have complete squares for two variables now by combining the x terms and combining the y terms separately.

Answer 5

\[9x ^{2} + 4y ^{2} - 54x + 24y + 81 = 0\]\[9x ^{2} - 54x + 4y ^{2} + 24y = -81\]\[9x ^{2} - 54x + 81 + 4y ^{2} + 24y + 36 = -81 + 81 + 36 = 36\]\[9(x ^{2} - 6x + 9) + 4 (y ^{2} + 6y + 9) = 36\] \[9(x-3)^{2} + 4(y+3)^{2} = 36\]\[\frac{ (x-3)^{2} }{ 4 } + \frac{ (y + 3)^{2} }{ 9 } = 1\] so after solving it my bad it is an ellipse