give a parametrization of the ellipse x^2/25 + y^2/9 =1 that travels once counter clockwise in an interval at belongs to (0, 2pi)?
after interval its not sorry its only "t"
(reiny) i need help please
To parametrize the ellipse x^2/25 + y^2/9 = 1, let's assign variables to x and y such that x = 5cos(t) and y = 3sin(t), where t is the parameter that varies within the given interval (0, 2π).
We chose x = 5cos(t) and y = 3sin(t) because these equations represent the standard parametric equations for an ellipse centered at the origin with a horizontal major axis of length 2a and a vertical minor axis of length 2b.
Here's how you can verify that these equations satisfy the equation of the ellipse:
(x^2/25) + (y^2/9) = (25cos^2(t)/25) + (9sin^2(t)/9) = cos^2(t) + sin^2(t) = 1.
Therefore, the parametrization of the ellipse, traveling once counter-clockwise in the interval (0, 2π), is:
x = 5cos(t)
y = 3sin(t)
As t varies from 0 to 2π, the parametric equations trace out the entire ellipse once counter-clockwise.