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Tangent to an Ellipse

This is an exploration of what is involved when you try to find the general function for the tangent to an ellipse. Since an ellipse is not a function, a piecewise function is required in order to determine the general function of the tangent. It is possible to determine each of the necessary functions individually, but with a little careful thought and consideration of concepts such as symmetry, it is possible to avoid doing this, resulting in a more complex understanding of what is going on.