Find the slope of a line tangent to the surface

Question 1

Slope of a tangent line: Basically, the slope of a tangent line to a curve is the ratio of the change in y co-ordinate to the change in x . But, in this problem, the slope is given by,

Question 2

Tangent:

Question 3

Find the slope of a line tangent to the surface z+x²+y²-6=0 and parallel to the xz-plane that passes through (1, 1, 1). Draw a sketch illustrating this problem

Answer to question 1

Given:

Answer to question 2

For the given:-

Answer to question 3