with(plots):
macro(palegreen=COLOR(RGB, .7, .9, .7),paleyellow=COLOR(RGB,.9,.9,.6));
For Reading Question #1
p1:=plot3d(-.5*x^2-.4*y^2+1, x=-2..2, y=-2..2, axes=normal, scaling=constrained):
p2:=plot3d(1, x=-2..2, y=-2..2):
display(p1,p2);
p3:=plot3d(-.5*x^2-.4*y^2+1, x=-.25.. .25, y=- .25.. .25, axes=normal, scaling=constrained):
p4:=plot3d(1, x=-.25.. .25, y=-.25.. .25):
display(p3,p4);
Finding the Tangent Plane:
f:= (x,y) -> -x^2/9-y^2/4+4;
p5:=plot3d([3*v*cos(u), 2*v*sin(u), -v^2+4], u=0..2*Pi, v=-2..2, axes=boxed, color=palegreen):
p7:=spacecurve([x,2,f(x,2)], x=-3*sqrt(3)..3*sqrt(3), color=navy, thickness=2):
p8:=arrow(<2,2,23/9>, <1,0,-4/9>, width=[.15, relative], head_length=[.4,relative], color=red):
display(p5,p7,p8);
p9:=spacecurve([2,y,f(2,y)], y=-8*sqrt(2)/3..8*sqrt(2)/3, color=violet, thickness=2):
p10:=arrow(<2,2,23/9>, <0,1,-1>, width=[.15, relative], head_length=[.4,relative], color=red):
display(p5,p9,p10);