find two sets of parametric equations for the given rectangular equation.

Question

x^2+4y^2-16=0

Answer 1

x^2 - 16 = 4y^2 or (x+4)(x-4) = 4y^2

let x = t
then
t^2 - 16 = 4y^2
y^2 = (t^2 - 16)/4
y = ± √(t^2 - 16)/2 , -4 ≤ t ≤ 4

Answer 2

x = 4cos(t)
y = 2sin(t)

x^2+4y^2 = 16cos^2(t)+16sin^2(t) = 16