Çözüldü Geometric Meaning of Partial Derivative in Three-Dimensional Coordinate System

A challenged adaptation of a solved problem from Metro State University:

If the surface (8x^2 + 2y^2 + 10z^2) / (xyz) = 13 implicitly defines z as a function of x and y, what is the slope of the tangent line parallel to the xz plane at the point (1, a, 1) of this surface when a is an integer?

A) -5 / 3
B) -3 / 5
C) 1 / 4
D) 3 / 7
E) 4 / 9

(8·1^2 + 2·a^2 + 10·1^2) / (1·a·1) = 13 ⇒ 2a^2 - 13a + 18 = 0 ⇒ a1 = 9 / 2 ∉ Z and a2 = 2 ∈ Z.

https://i.ibb.co/JwM8jTd1/Metro-State.png
https://wetalldid.wordpress.com/wp-...-w-solutions-2011-calculus-3-louis-talman.pdf
(Page 3, Question 5)