what equation belong? 4x^2+4x-24y=37

Question

Is it straight line,circle,parabola,ellipse,hyperbola

Answer 1

This should help:

Answer 2

It's a parabola: 24y=4x^2+4x-37,

24y=4(x^2+x)-37,

24y=4(x^2+x+1/4)-1-37,

24y=4(x+1/2)^2-38,

24y+38=4(x+1/2)^2,

12y+19=2(x+1/2)^2 or y+19/12=(1/6)(x+1/2)^2.

Vertex is (-1/2,-19/12).