Parametric equations for circles and ellipses: plot, directionality and eliminating the parameter.

New videos every week! Subscribe to Zak's Lab    / @zakslab   Questions or requests? Post your comments below, and I will respond within 24 hours. We start by plotting the unit circle given in parametric form. By plotting several specific points, we can determine the directionality of the curve. Then we eliminate the parameter to arrive at the standard formula for the unit circle in rectangular coordinates. Next, we generalize to the parametric equations for an ellipse, in which the minimum and maximum values of x and y are simply stretched out to the semi-major and semi-minor axes of the ellipse. Again, we determine directionality using a few explicit points, and we eliminate the parameter to retrieve the standard rectangular form of the equation of an ellipse.