9x^2 + 16y^2 - 18x - 64y - 71 = 0 write equation in standard form for the ellipse described

Question

what is this

Answer 1

9x^2 + 16y^2 - 18x - 64y - 71 = 0
(9x^2 - 18x) + (16y^2 - 64y) - 71 = 0
9(x^2 - 2x) + 16(y^2 - 4y) = 71
9(x - 1)^2 - 9 + 16(y - 2)^2 - 64 = 71
9(x - 1)^2 + 16(y - 2)^2 - 73 = 71
9(x - 1)^2 + 16(y - 2)^2 = 71 + 73
9(x - 1)^2 + 16(y - 2)^2 = 144
[9(x - 1)^2 / 144] + [16(y - 2)^2 / 144] = 1
[(x - 1)^2 / 16] + [(y - 2)^2 / 9] = 1
[(x - 1)^2 / 4^2] + [(y - 2)^2 / 3^2] = 1, which is the form we need.