Question

4y^2-x^2+4=0 is it a circle, ellipse, parabola or hyperbola

Answer 1

hyperbola

Answer 2

hyperbola

Answer 3

This is a hyperbola. Whenever you are asked to classify an equation (where both the x term and the y term are squared) you can do so by rewriting the equation so that the constant term is positive and by itself on one side of the equation. Then look at what's on the non-constant side: here you'd get x^2 - 4y^2 = 4 : a difference of two squares on the left side tells me it's a hyperbola. If it was a sum - then it would either be a circle or an ellipse. It can't be a parabola because the equation for a parabola has only one variable term squared.