k = 3 (slider from -5 to 5)
f(x, y) = If[5 - (x - 9)^(2) / 15 - (y - 5)^(2) / 14 > 1.5, 5 - (x - 9)^(2) / 15 - (y - 5)^(2) / 14]
A = (8.974814298749937, -0.29329508824958594, 0)
B: (x(A), y(A), f(x(A), y(A)))
fx = Derivative(f, x)
fy = Derivative(f, y)
a: f(x(A), y(A))
b: f(x(A), y(A))
g: z = k
t(x, y) = If[abs(x - x(A)) < 3 ∧ abs(y - y(A)) < 3, f(x(A), y(A)) + (fx(x(A), y(A)) * (x - x(A))) + (fy(x(A), y(A)) * (y - y(A)))]
gl2 = IntersectPath(g, t)
gl1 = IntersectPath(g, z = 3)
gl3 = IntersectPath(g, z = k)
gl4 = IntersectPath(g, f)
C = PointIn(t)
u = Vector(B, C)