(Solved): In part a), i believe the point is (0,1, +-sqr(3)), but what is this angle means? Consider ...

In part a), i believe the point is (0,1, +-sqr(3)), but what is this angle means?

Consider the ellipse formed by the intersection of the plane $$y=1$$ with the ellipsoid $$3x^2+4y^2+4z^2=16$$ (a) Determine the points on the ellipse closest to the $$y$$-axis and the angles it makes with this axis. Reminder that answers need to be supported by work. This answer should require plenty of pictures, some algebra, and a fair bit of writing. Hint: Different viewpoints of the graph helps give solutions to different parts of the problem. You can try using Geogebra 3D to get an idea of the problem, but a submitted solution relying on Geogebra will not be accepted (see conditions above on assignment expectations). Try to get an overall idea by graphing the two surfaces before you begin writing. Then graph the ellipse formed in the plane $$y=1$$ by determining an appropriate $$xz$$ equation. Then examine the graph in the $$yz$$-plane. (b) In Calculus II, we have learned that curves can be described by a set of parametric equations $$x=f(t)$$, $$y=g(t),z=h(t)$$, etc. Determine a single set of parametric equations (no roots with the plus/minus nonsense) that gives this ellipse. Verify your answer by showing they satisfy both surface equations. Hint: You may need to review the standard parametric equations for a circle and how it extends to an ellipse.