Chapter 13.7, Problem 60E

(a)

To determine

To graph: The surfaces given by the function $f\left(x,y\right)=\sqrt{16-x^2-y^2+2x-4y}$ and $g\left(x,y\right)=\frac{\sqrt{2}}{2}\sqrt{1-3x^2+y^2+6x+4y}$ in the first octant.

(b)

To determine

To calculate: One point that lies on the intersection of the curves $f\left(x,y\right)=\sqrt{16-x^2-y^2+2x-4y}$ and $g\left(x,y\right)=\frac{\sqrt{2}}{2}\sqrt{1-3x^2+y^2+6x+4y}$ in the first octant and to show that at this point both the curves are orthogonal.

(c)

To determine

Whether the surfaces $f\left(x,y\right)=\sqrt{16-x^2-y^2+2x-4y}$ and $g\left(x,y\right)=\frac{\sqrt{2}}{2}\sqrt{1-3x^2+y^2+6x+4y}$ are orthogonal along all the point on the intersection.