Answer:
E(t) = [ 4cos(t) , 2 sin(t) ]
Step-by-step explanation:
The elipse ecuacion is of the form:
(x² ÷ a² ) + (y² ÷ b² ) = 1 Where a and b are the horizontal and vertical semi-diameters respectively
In our particular case x²/16 + y²/ 4 = 1
That form suggests (x/a)² + (y/b)² =1
And again in our case x²/16 + y²/4 = 1 the same shape of sin²α +cos²α = 1
So we call x = 4 cos(t ) and the
We need to find y
x²/16 + y²/4 = 1
x²/16 + y²/4 = 1 ⇒ (x² + 4y²) ÷ 16 = 1
Solving for y (x² + 4y²) = 16 ⇒ y² = ( 16 - x²) ÷4
as x = 4 cos(t) ⇒ y² = (16 - 16cos²(t)) ÷ 4 y = √4 (1 -cos²(t)
y = 2 sin (t)
So the vector parametrization of the elipse is
E(t) = [ 4cos(t) , 2 sin(t) ]
