Final answer:
The parametric equations given, x=cos(θ) and y=2sin(2θ), do not directly suggest one of the conic sections (circle, ellipse, parabola, hyperbola) without additional context or manipulation to eliminate the parameter θ and find a direct relationship between x and y.
Step-by-step explanation:
The given parametric equations x=cos(θ) and y=2sin(2θ) do not represent any of the conic sections (circle, ellipse, parabola, or hyperbola) directly in their given form. To determine the shape these equations represent, one could attempt to eliminate the parameter θ to find a relationship directly between x and y. However, due to the nature of the functions involved (cosine function for x and a sine function with a different argument for y), it is not straightforward to eliminate the parameter without additional context or information. While conic sections such as the circle, ellipse, parabola, and hyperbola are described by specific algebraic equations and geometric properties, these parametric equations do not immediately suggest any of these shapes. The relationship between x and y given by these equations will produce a graph that is periodic and related to the trigonometric functions, but further elaboration or another form of the equations would be needed to correctly identify the specific type of curve that is represented.