Slope of tangent line to curves cut from surface

[chetzread]

Homework Statement

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 ...

Homework Equations

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

 

[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

 

[chetzread]

So

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

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

 

[FactChecker]

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 . ?

yes