eliminate the parameter t for x=3sint and y=2cost

Question

eliminating the parameter

Answer 1

All we need to do is make use of the identity

sin² t + cos² t = 1

To do this we will square both parametric equations to get

x² = 9 sin² t    and    y² = 4 cos² t

x²/9 = sin² t    and    y²/4 = cos² t

Now wee add the two equations

x²/9 + y²/4 = sin² t + cos² t

(x/3)² + (y/2)² = 1

Answer 2

t=sin^-1(x/3)=cos^-1(y/2)

sin^-1(x/3)-cos^-1(y/3)=0

Answer 3

sin^2 t + cos^2 t = 1

So, (x/3)^2 + (y/2)^2 = 1, since sint = x/3, and cost = y/2

This is an ellipse with major axis on x-axis.