When x = a cos(t) and y = b sin(t), the trajectory traced out is an ellipse. The values of a and b determine the size and orientation of the ellipse. The major axis of the ellipse is 2a units long, and the minor axis is 2b units long. The eccentricity of the ellipse is given by e = √(1 - (b^2 / a^2)), where e measures how elongated or flattened the ellipse is.
If a > b, the ellipse will be stretched more in the x-direction, resulting in a more elongated ellipse. If a < b, the ellipse will be stretched more in the y-direction, resulting in a more flattened ellipse. If a = b, the ellipse will be a circle.
In summary, the values of a and b determine the size, shape, and orientation of the ellipse traced out by the parametric equations.
For parametric equations x = a cost and y = b sin t, describe how the values of
a and b determine which conic section will be traced.
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