2314-Tangent Plane to a Surface in $\mathbb{R}^3$.sagews

Tangent Plane to a Surface in $\mathbb{R}^3$

The surface, in blue, is the graph of $z = x^2 + y^2$.

The point of tangency, in red, is $(1, 2, 5)$.

The tangent plane, in yellow, is $z = 2x + 4y - 6$, in yellow.

x, y = var('x,y')
P = plot3d(x^2 + y^2, (x,-4,4), (y,-4,4), opacity=0.7)
Q = plot3d(2*x + 4*y - 6, (x,-4,4), (y,-4,4), opacity=0.7, color='yellow')
S = sphere((1,2,5),size=0.1, color='red', aspect_ratio=1)
P + Q + S