Question 133096
<pre>
How do you identify whether {{{x^2+3y^2-2x+36y+100=0}}} is a circle, 
hyperbola, parabola, or an ellipse.
<font size = 4 color = "indigo"><b>

Rule:

For the equation:

{{{Ax^2 + Cy^2 + Dx + Ey + F = 0}}}

1. If A = C, the equation is of a circle
2. If A or C is 0 but not both 0 the equation is of a parabola.
3. If A and C have the same sign, but are not equal, the equation is of an ellipse.
4. If A and C have opposite signs, the equation is of a hyperbola.


Your equation is

{{{x^2 + 3y^2 - 2x + 36y + 100=0}}}

Comparing that to

{{{Ax^2 + Cy^2 + Dx + Ey + F = 0}}}

{{{A=1}}}, {{{C=3}}} (It doesn't matter about {{{D}}}, {{{E}}}, and {{{F}}})


A and C have the same sign but they are not equal, so the graph is of
an ellipse.

Edwin</pre>