The parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
Path of the parametric equations
The given parametric equation can be expressed as follows;
x = 3 + cosθ
y = 2sinθ
From the given options, a plot of the various equation can be used to determine the paths of the equation.
For; x = 3 + cos(2θ) and y = 2sin(2θ), its parametric plots is same as original equation since the equation [3 + cos(2θ) and y = 2sin(2θ)] changed at equal rate of the angles.
Thus, the parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
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