eliminate the parameter to find a cartesian equation of the curve for x=2cos(θ), y=3sin(θ)

Answer 1

We can use the identity cos^2(θ) + sin^2(θ) = 1 to eliminate θ:

x^2/4 + y^2/9 = cos^2(θ) + sin^2(θ) = 1

Multiplying both sides by 36, we get:

9x^2 + 4y^2 = 36

Dividing both sides by 36, we get the final cartesian equation:

x^2/4 + y^2/9 = 1