Why is ContourPlot not displaying this curve?

Question

I am using the general form of a second-degree plane curve:

$$Ax^2+2Bxy + Cy^2+2Dx + 2Ey + F = 0$$

I want to randomly generate plane curves of this form, so I am using RandomReal[{-1,1},6] to
generate the coefficients. I made the above equation into a function:

SecondDegreeCurve[{a_, b_, c_, d_, e_, f_}, x_, y_] := 
   a x^2 + 2 b x y + c y^2 + 2 d x + 2 e y + f == 0

However, when I try to plug the composition

ContourPlot[
 SecondDegreeCurve[RandomReal[{5}, 6], x, y], 
 {x, -2, 2}, {y, -2, 2}]

into ContourPlot, the image comes back blank.

When I run SecondDegreeCurve[RandomReal[{5}, 6], x, y], I get something like the following output:

1.4557 + 5.20582 x + 1.29609 x^2 + 9.37565 y + 6.73248 x y + 1.84528 y^2 == 0

and when I plug this into ContourPlot, the curve is displayed.

My question is, what is it about the initial composed expression that doesn't display the curve?

Answer 1

This has to do with the HoldAll attribute of ContourPlot. Try it with Evaluate inserted, like this:

ContourPlot[
   SecondDegreeCurve[RandomReal[{5}, 6], x, y] // Evaluate,
   {x, -2, 2}, {y, -2, 2}
]

you get ouput like this:

or

Answer 2

Evaluate works. I prefer Function:

SecondDegreeCurve[{a_, b_, c_, d_, e_, f_}, x_, y_] := 
  a x^2 + 2 b x y + c y^2 + 2 d x + 2 e y + f == 0

ContourPlot[#, {x, -2, 2}, {y, -2, 2}] & @
  SecondDegreeCurve[RandomReal[{5}, 6], x, y]

Answer 3

Use Evaluate, i.e.

ContourPlot[Evaluate @ SecondDegreeCurve[RandomReal[{5}, 6], x, y] == 0, 
   {x, -2, 2}, {y, -2, 2}]