Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. I'm not sure that this is an 'easy' exercise, exactly, at least not at the level one would encounter such a problem, but the difficulties are more computational than conceptual. In our situation, as is often the case, it's easier to make a change of coordinates in which the expressions for the surfaces are easier to work with; once we've parameterized the intersection in the new coordinates, if we'd like we can produce a parameterization in the given coordinates simply by reversing the changes of variable.
5.3: Line Integrals
calculus - Parametrize the curve of intersection of 2 surfaces - Mathematics Stack Exchange
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Given it is a circumference, we can parametrize it by. Sign up to join this community. The best answers are voted up and rise to the top.
This equation is very similar to the one used to define a circle, and much of the discussion is omitted here to avoid duplication. See Parametric equation of a circle as an introduction to this topic. The only difference between the circle and the ellipse is that in a circle there is one radius, but an ellipse has two:. Note that the equations on this page are true only for ellipses that are aligned with the coordinate plane, that is, where the major and minor axes are parallel to the coordinate system. In the applet above, drag one of the four orange dots around the ellipse to resize it, and note how the equations change to match.
In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Consider the orbit of Earth around the Sun. Our year lasts approximately