Slope of tangent line to curves cut from surface

1. Oct 12, 2016

1. The problem statement, all variables and given/known data
find the slope of tangent line to curves cut from surface z = (3x^2) +(4y^2) - 6 by planes thru the point (1,1,1) and parallel to xz planes and yz planes ...
2. Relevant equations

3. The attempt at a solution
slope of tnagent that parallel to xz planes is dz/dy , while the slope of tangent that parallel to yz plane is dz /dz . Correct me if i am wrong

Last edited by a moderator: Oct 13, 2016
2. Oct 13, 2016

FactChecker

To be parallel to the xz plane means that the y value is some constant number (y ≡ 1). So there is no dy. y is not involved in that slope except that its constant value (1) might be in the equation. Calculate dz/dx and plug in the 1s.
Similarly, to be parallel to the yz plane means that the x value is some constant number (x ≡ 1). So there is no dx. x is not involved in that slope except that its constant value (1) might be in the equation. Calculate dz/dy and plug in the 1s

3. Oct 13, 2016

So
So , slope of tnagent that parallel to xz planes is dz/dx , while the slope of tangent thatparallel to yz plane is dz /dy . ???

4. Oct 13, 2016

yes