Please post source text or maple worksheet.

Which parameter is to vary? Is it phi?

** restart;
with(plots);
local O;
P := b*x*cos(phi) + a*y*sin(phi) - a . b = 0;
Q := a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi) = 0;
M := op(solve([P, Q], [x, y]));
X := `&-+`((P)/(sqrt(b^2*cos(phi)^2 + a^2*sin(phi)^2)));
Y := `&-+`((Q)/(sqrt(b^2*cos(phi)^2 + a^2*sin(phi)^2)));
(P^2)/(A*(b^2*cos(phi)^2 + a^2*sin(phi)^2))
+ (Q^2)/(B*(b^2*cos(phi)^2 + a^2*sin(phi)^2)) - 1 = 0;
a := 10;
b := 7;
c := sqrt(a^2 - b^2);
phi := 4/5*Pi;
Ell := plots:-implicitplot((x^2)/(a^2) + (y^2)/(b^2) - 1 = 0, x = -11 .. 11,
y = -8 .. 8, color = grey);
O := [0, 0];
M := [a*cos(phi), b*sin(phi)];
vec := plot([O, M], color = black, thickness = 1);
P := plots:-implicitplot(P, x = -20 .. 20, y = -20 .. 20, color = aquamarine);
Q := plots:-implicitplot(Q, x = -20 .. 20, y = -20 .. 20);
F1 := [(a + b)*cos(phi), (a + b)*sin(phi)];
F2 := [2*M[1] - F1[1], 2*M[2] - F1[2]];
F1F2 := plot([F1, F2], color = green, thickness = 3);
ELL := plots:-implicitplot(((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))^2)/(
a^2*(b^2*cos(phi)^2 + a^2*sin(phi)^2)) + (
(a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))^2)/(c^2*cos(phi)^2*(
b^2*cos(phi)^2 + a^2*sin(phi)^2)) - 1 = 0, x = -20 .. 20, y = -20 .. 20,
color = blue, thickness = 3);
Hyp := plots:-implicitplot(((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))^2)/(
b^2*(b^2*cos(phi)^2 + a^2*sin(phi)^2)) - (
(a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))^2)/(c^2*sin(phi)^2*(
b^2*cos(phi)^2 + a^2*sin(phi)^2)) - 1 = 0, x = -20 .. 20, y = -20 .. 20,
color = black);
dF1 := plottools[disk](F1, 0.3, color = red);
dF2 := plottools[disk](F2, 0.3, color = red);
cir1 := plots:-implicitplot(x^2 + y^2 = (a + b)^2, x = -20 .. 20,
y = -18 .. 18, color = pink);
cir2 := plots:-implicitplot(x^2 + y^2 = (a - b)^2, x = -10 .. 10,
y = -4 .. 4, color = coral);
asym1 := plots:-implicitplot((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))/(b)
+ (a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0,
x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT);
asym2 := plots:-implicitplot((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))/(b)
- (a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0,
x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT);
tp := plots:-textplot([[M[1], M[2] + 0.8, "M"], [F1[1] - 0.8, F1[2], "F1"],
[F2[1] + 0.8, F2[2] + 0.3, "F2"], [5, 15, "axe P"], [8, -10, "axe Q"]]);
plots:-display(
[Ell, vec, P, Q, F1F2, cir1, cir2, ELL, Hyp, dF1, dF2, asym1, asym2, tp],
scaling = constrained, axes = normal,
axis = [gridlines = [1, color = blue]], xtickmarks = 0, ytickmarks = 0,
view = [-20 .. 20, -20 .. 20], size = [500, 500]);
**