How can I plot a line on a plane?

If I have a plane in this following format z = f(x,y) = a + b*x + c*y + d*x^2 + e*x*y + f*y^2 and I have a line in y=f(x) = p1*x^2 + p2*x + p3 format, how can I plot the line on the plane?

For example, if I use hold on to try to plot the two together, the f(x) line gets plotted two-dimensionally flat in z = 0 plane. Instead of the z = 0 plane I would like a specific plane of z = a + b*x + c*y + d*x^2 + e*x*y + f*y^2 format.

It would be better if I could somehow combine the two equations and turn it into a 3D line and only plot that if possible.

[KSSV]

Show us the code you have tried.

Answer 1

[Walter Roberson]

C = randi([-9 9], 1, 9);
a = C(1), b = C(2), c = C(3), d = C(4), e = C(5), f = C(6), p1 = C(7), p2 = C(8), p3 = C(9)

a = 2

b = -6

c = 5

d = 1

e = -7

f = -9

p1 = 5

p2 = -2

p3 = -5

syms x y
z = a + b*x + c*y + d*x^2 + e*x*y + f*y^2

z = 

y1 = p1*x^2 + p2*x + p3

y1 = 

y2 = solve(z == y1, y)

y2 = 

z21 = simplify(subs(z, y, y2(1)))

z21 = 

z22 = simplify(subs(z, y, y2(2)))

z22 = 

fsurf(z, [-10 10], 'edgecolor', 'none');
hold on
fplot3(x, y2(1), z21, [-10 10])
fplot3(x, y2(2), z22, [-10 10])
hold off

Answer 2

[DGM]

There are probably a bunch of ways to do this, but I did this:

% plot range
xrange = [-5 5];
yrange = [-5 5];

% I choose to use parameter vectors
a = [1 1 1 1 1 1];
p = [1 1 1]

syms x y
% a surface
z1 = a(1) + a(2)*x + a(3)*y + a(4)*x.^2 + a(5)*x.*y + a(6)*y.^2
% a curve in the x-y plane
y1 = p(1)*x.^2 + p(2)*x + p(3)
% the projection of y1 on z1
z2 = subs(z1,y,y1)

% curve extends beyond plot range, so find the parameter limits for fplot3
% if it extends beyond other edges, you'll have to solve for that too
curvelimits = double(solve(y1==5,x))'; % limiting values of x

h1 = fsurf(z1,[xrange yrange],'edgecolor','none'); hold on
fplot3(x,y1,z2,curvelimits,'linewidth',3)
fplot(x,y1,curvelimits)