Find an equation of the tangent line to the curve of intersection of the surface z=f(x,y)=16−x2−y2:
Symmetric equations of a line in space are discussed in Section 10.6, pp. 734–735.
(b) The slope of the tangent line to the curve of intersection of z=16−x2−y2 and the plane x=1 at any point is fy(1,y)=−2y. At the point (1,2,11), the slope is fy(1,2)=−2(2)=−4. This tangent line lies on the plane x=1. Symmetric equations of the tangent line are z−11=y−2−1/4x=1