Question

Without writing the equation 4y^2-x^2+4=0 in the standard form, state whether the graph of this equation is a parabola, circle, ellipse, or hyperbola.

Answer 1

It's not a circle because the coefficient of y^2 is not equal to coefficient of x^, namely 4 is not equal to -1

Answer 2

do you know what it is?

Answer 3

thanks for the reply anyways!

Answer 4

Please put your equation in the form: ax^2+bxy+cy^2+dx+ey+f=0
where a,b,c,d,e,f are coefficient. In our case we have:
x^2-4y^2-4=0, so
a=1,
b=0,
c=-4,
d=0,
e=0,
f=-4
then, evaluate this quantity:
\[\Delta=b ^{2}-4*a*c\]
if \[\Delta <0\] we have an ellipse,
if \[\Delta=0\] we have a parabola,
if \[\Delta > 0\] we have an hyperbola.
So try to calculate \[\Delta \] and write your answer, please