Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter 16 along the x-axis, minor diameter 12 along the y-axis, and is oriented counter-clockwise. Your parametrization should make the point (8,0) correspond to t= 0.

x(t) =
y(t) =

(0 <= t <= 2π).

Step-by-step explanation:

1) Firstly, the basic relations when it comes to parametrization:

2) The given ellipse:

3) Let's parametrize it:

a, b for the radii, and p, and q since it is centered at the origin then p and q i equal to zero. a =

Then parametrized:

Lastly, on the right the parametric curve where (8,0) t=0

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: