Ellipse a. Show that the curve is an ellipse by showing

Chapter 12, Problem 17E

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Ellipse a. Show that the curve is an ellipse by showing that it is the intersection of a right circular cylinder and a plane. Find equations for the cylinder and plane.b. Sketch the ellipse on the cylinder. Add to your sketch the unit tangent vectors at and c. Show that the acceleration vector always lies parallel to the plane (orthogonal to a vector normal to the plane). Thus, if you draw the acceleration as a vector attached to the ellipse, it will lie in the plane of the ellipse. Add the acceleration vectors for and to your sketch.d. Write an integral for the length of the ellipse. Do not try to evaluate the integral; it is nonelementary.e. Numerical integrator Estimate the length of the ellipse to two decimal places.