what is wrong with this question?
The equation $y^2+4y+4x^2+4x+21=0$ can be changed into a vertex equation by completing the square. Which conic section can be made from the graph of this equation? A. ellipse B. hyperbola C. circle D. parabola

Question

what is wrong with this question?
The equation $y^2+4y+4x^2+4x+21=0$  can be changed into a vertex equation by completing the square. Which conic section can be made from the graph of this equation? A. ellipse B. hyperbola C. circle D. parabola

anonymous · Answer

Calculate the Discriminant. It is an ellipse.

anonymous · Answer

no actually it isn't

anonymous · Answer

Ok...

anonymous · Answer

question was just asked here
it was i guess supposed to be an ellipse, but if you complete the square you see it is nothing

anonymous · Answer

You are trying to recover it in the standard form of ellipse
$$\frac{ x^2 }{a^2 } + \frac{ y^2 }{ b^2 } = 1$$ ?

hero · Answer

http://www.wolframalpha.com/input/?i=y%5E2%2B4y%2B4x%5E2%2B4x%2B21

anonymous · Answer

If you calculate its determinant, it comes out to be positive. This is the condition for a degenerate ellipse. So there are no real points to plot it. I don't know how wolframalpha engine is plotting it ! I think it is treating x as a variable and y as a parameter.

anonymous · Answer

How is that plotting a 3D structure ?

anonymous · Answer

Oh! In wolframalpha engine you need to search for y^2+4y+4x^2+4x+21 = 0, which is an equation. You have put an expression y^2+4y+4x^2+4x+21 there.