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from manimlib.imports import*
class TangenttoSurface(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
#----f(x,y): x**2+y**2
p = ParametricSurface(
lambda u, v: np.array([
u,
v,
u**2+v**2
]),v_min = -1,v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_C,GREEN_D],
resolution = (20, 20)).scale(1)
self.set_camera_orientation(phi = 75*DEGREES)
h_text = TextMobject("The graph tends to coincide with its tangent plane").scale(0.5).to_corner(UL)
d = Dot([0,0,0],color ='#800000') #----critical point
r = Rectangle(height = 2,breadth = 1,color = YELLOW).scale(0.5) #----tangent plane to critical point
line1 = DashedLine(color=RED).shift(4*UP+1.3*RIGHT).rotate(1.571,UP).scale(1.2)
line2 = DashedLine(color=RED).shift(4*UP-1.3*RIGHT).rotate(1.571,UP).scale(1.2)
r2 = Rectangle(height = 2, breadth = 1,color = GREEN, fill_opacity=0.3).scale(0.5)
self.add(axes)
self.play(Write(r))
self.play(Write(p),Write(d))
self.play(ShowCreation(line1),ShowCreation(line2))
self.wait(2)
self.play(FadeOut(line1),FadeOut(line2),ReplacementTransform(p,r2))
self.add_fixed_in_frame_mobjects(h_text)
self.wait(1)
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