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

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3 Answers

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 cost

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

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

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

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.