Complete the square to determine whether the equation represents an ellipse, parabola, or hyperbola?

Question

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

This is related to conics

Answer 1

you do not even need to complete the square,
your equation is the one of an ellipse

9x^2-36x+4y^2=0
9(x^2-4x+4)+4y^2=0
9(x-2)^2+4y^2=36
dividing by 36
(x-2)^2/4 + (y^2)/9 = 1
:D

Answer 2

9x^2-36x+4y^2=0
(9x^2-36x+__)+4y^2=0
9(x^2-4x+4)+4y^2=0
9(x-2)^2+4y^2=36
Divide everything by 36
(x-2)^2/4 + (y^2)/9
Its an ellipse

Answer 3

-4y^2= 9x(x-4)
y^2= 9x(x-4)/(-4)
y=sqr{9x(x-4)/(-4)}
it is an U shape, i forgot the name