Question

Put the equation in standard form for an ellipse.
9x^2-54x+16y^2+32y=47

Answer 1

Complete the square :P Do you know how to do that?

Answer 2

use completing the square
1)First factor out the leading coefficients
-> 9(x^2-6x) + 16(y^2+2y) = 47
2)complete the square (half of b, then subtract the square)
->9[(x-3)^2 -9] + 16[(y+1)^2 -1] = 47
3)distribute the leading coefficients
-> 9(x-3)^2 -81 +16(y+1)^2 -16 = 47
4)move all constants to right hand side
->9(x-3)^2 + 16(y+1)^2 = 144
5)divide by 144 so there is 1 on right hand side
->9/144(x-3)^2 + 16/144(y+1)^2 = 1
6) Reduce
\[\frac{(x-3)^{2}}{16} + \frac{y+1)^2}{9} = 1\]