Is this a ellipse or hyperbola?

Question

y^2/4 + x^2/16 = 1

i think its a ellipse and that the y and x intercepts are

(0,2) (0,-2)

(4,0) (-4,0)

but im not sure if thats right since i confuse ellipses and hyperbolas whats the difference between the two? and did i do that problem right??

Answer 1

If the x² and y² terms have the same sign, it's an ellipse.

If they have different signs, it's a hyperbola.

y²/4 + x²/16 = 1  is an ellipse. Note that in conventional form the equation would be written

    x²/4² + y²/2² = 1

    denominators expressed as squares

    the term with the larger denominator comes first

vertex at (0,0)

When x=0, y²=2²  ⇒  y=±2  ⇒  x-intercepts (0,-2) and (0,2).

When y=0, x²=4²  ⇒  x=±4  ⇒  y-intercepts (-4,0) and (4,0).

Yep, you got it right!  :)

Answer 2

ellispes are skinnier than hyperbola's. this is a hyperbola

Answer 3

correct

a hyperbola has a negative between the 2 fractions

well done u did it ok.