Chapter 13.7, Problem 59E

(a)

To determine

To calculate: The parametric equations for the tangent line to the curve at the intersection of the function f and g that passes through the point $\left(1,2,4\right)$ and the angle of intersection between the gradient of two curves $f\left(x,y\right)=6-x^2-\frac{y^2}{4}$ and $g\left(x,y\right)=2x+y$.

(b)

To determine

To graph: The surfaces and the tangent line where the functions $f\left(x,y\right)=6-x^2-\frac{y^2}{4}$ and $g\left(x,y\right)=2x+y$. The parametric equation of the tangent line as $x=t+1,y=-2t+2,z=4$.