Question 290936
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Rule:

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

Then look for the terms in {{{x^2}}} and {{{y^2}}}

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.

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

It already has all the terms on one side with a 0 on the right
Neither the {{{x^2}}} term or the {{{y^2}}} term is missing and they
both have the same sign, so #3 above applies and the equation 
represents an ellipse.

Edwin</pre>