What is a parametric equation the defines the conic section

Question

(x²/16)+(y²/25)=1

Answer 1

Note that the given equation is of the form

 

x²/b² + y²/a² = 1 with a = 5 and b = 4

 

That defines an ellipse centered at the origin with semi-minor axis of 4 along the x-axis and semi-major axis of 5 along the y-axis.  Then

 

x(t) = b cos t = 4 cos t

y(t) = a sint t = 5 sin t

 

where t is the angle measured counterclockwise from the +x direction. 

Answer 2

x = 4 cos t

y = 5 sin t