Using Functions Consider the functions and (a) Use a computer algebra system to graph

Chapter 13, Problem 60

(choose chapter or problem)

Consider the functions

\(f(x, y)=\sqrt{16-x^{2}-y^{2}+2 x-4 y}\)

and

\(g(x, y)=\frac{\sqrt{2}}{2} \sqrt{1-3 x^{2}+y^{2}+6 x+4 y}\) .

(a) Use a computer algebra system to graph the first-octant portion of the surfaces represented by f and g.

(b) Find one first-octant point on the curve of intersection and show that the surfaces are orthogonal at this point.

(c) These surfaces are orthogonal along the curve of intersection. Does part (b) prove this fact? Explain.

Text Transcription:

f(x, y) = sqrt{16 - x^2 - y^2 + 2x - 4y}

g(x, y) = {sqrt{2} / 2 sqrt{1 - 3x^2 + y^2 + 6x + 4y}