f(x, y) = (0.25 * x^(2)) + (0.5 * y^(2)) - 1
k_h = 1.5 (slider from -5 to 5, step 1)
f_x = Derivative(f, x)
x_h = 3.25 (slider from -8 to 8, step 0.25)
A: (x_h, k_h, f(x_h, k_h))
d_x: f_x(x_h, k_h)
h: y = k_h
a = IntersectPath(h, f)
r_0 = Line((0, 0, 0), Vector[(1, 0, f_x(x_h, k_h))])
B: (x(A), y(A))
texto1: "P_0(" + (LaTeX[x_h]) + "," + (LaTeX[k_h]) + ")"
u: (1 / sqrt(5), 2 / sqrt(5))
i: (1, 0, 0)
k: (0, 0, 1)
j: (0, 1, 0)
r_y = Line((3.25, 1.5), j)
plano2: x + (0 * y) + (0 * z) = 3.25
ec1 = IntersectPath(plano2, f)
f_y(x, y) = y
r_1 = Line((0, 0, 0), Vector[(0, 1, f_y(x_h, k_h))])
t_{A,y} = Line(A, r_1)
r_u = Line((3.21, 1.5, 0), u)
p = Plane(A, r_u)
ec2 = IntersectPath(p, f)
d_u(x, y) = ((f_x(x, y), f_y(x, y)) * u)
Tangent(A, ec2)
r_{t} = Line((0, 0, 0), (1 / sqrt(5), 2 / sqrt(5), 4.625 / sqrt(5)))
t_{A,u} = Line(A, r_{t})
t_{A,x} = Line((x_h, (k_h * 0)), r_0)
r_x = Line((3.25, 1.5, 0), i)