Chapter 12.6, Problem 47E

Level curves Consider the upper half of the ellipsoid $f\left(x,y\right)=\sqrt{1-\frac{x^2}{4}-\frac{y^2}{16}}$ and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P and verify that the tangent line is orthogonal to the gradient at that point.

47.     $f\left(x,y\right)=\sqrt{3}/2;P\left(1/2,\sqrt{3}\right)$