Question

Find the center, vertices, foci, and eccentricity of the ellipse.

9x^2 + 4y^2 - 36x + 8y + 31 = 0

My answer was:
center=(2,1)
v=(-2,10)(-2,-10)
f=(-2,11)(-2,-11)
e=11/3

Where did I make a mistake?

Answer 1

9x^2 + 4y^2 - 36x + 8y + 31 = 0
9(x^2 - 4x + ...) + 4(y^2 + 2y + ...) = -31
9(x^2 - 4x + 4) + 4(y^2 + 2y + 1) = -31+36+4
9(x-2)^2 + 4(y+1)^2 = 9
(x-2)^2 + (y+1)^2 /(9/4) = 1

my centre is (2,-1)
a^2 = 1
b^2 = 9/4) etc

have you found your error?

Answer 2

9^2-[(4.2x3.4)-9.28