SOLUTION: Which conic section is represented by 4x^2+9y^2-8x-36y+4=0

Rule:

Get all the terms on one side with a 0 on the other side.

Then look for the terms in  and 

1.  If both are missing the equation represents a line.
2.  If one of them is missing, the equation represents a parabola.
3.  If neither is missing and they have the same sign, the equation
    represents an ellipse.
4.  If neither is missing and they have the opposite signs, and 
    the equation represents a hyperbola.



It already has all the terms on one side with a 0 on the right
Neither the  term or the  term is missing and they
both have the same sign, so #3 above applies and the equation 
represents an ellipse.

Edwin