Filling area common to two inequalities?

I am having two inequalities (one is explicit and another in implicit) and I want to fill the area common to these. I have drawn the corresponding equations in matlab but do not know how can I fill the common area. I am also uploading the image in which coloured their common area with help of paint. My code is:

clc;
clear all;
E11=0.041057; E12=-0.117734; E21=0.029952; E22=-0.042564;
A=[1 -E22/E11];
D0=E11*E22-E12*E21

x = linspace(-1, 7);                    % Row Vector
y1=max(A)*x  ;
F=@(x,y) E11.^2*y.^2+E22.^2*x.^2+(2*x.*y.*E11.*E22-4.*x.*y.*D0);

plot(x, y1,'--b','linewidth',1.3)
hold on
fimplicit(F,[0 7 0 20],'--r','linewidth',1.3)

xlim([0,7])
ylim([0,20])

I want to fill the area in which y1>0 and F>0 which is filled with orange color in below image.

Answer 1

[KSSV]

clc;
clear all;
E11=0.041057; 
E12=-0.117734; 
E21=0.029952; 
E22=-0.042564;

A=[1 -E22/E11];

D0=E11*E22-E12*E21 ;

x1 = linspace(-1, 7);                    % Row Vector
y1=max(A)*x1  ;

F=@(x,y) E11.^2*y.^2+E22.^2*x.^2+(2*x.*y.*E11.*E22-4.*x.*y.*D0);
[X,Y]  = meshgrid(linspace(0,7),linspace(0,20)) ;
F = F(X,Y) ; 
[c,h] = contour(X,Y,F,[0 0]) ; 

c(:,1) =[] ;
x2 = c(1,:) ;
y2 = c(2,:) ; 

plot(x1, y1,'--b','linewidth',1.3)
hold on
plot(x2,y2,'--r','linewidth',1.3)

xlim([0,7])
ylim([0,20])

Now you have the coordinates (x1,y1) and (x2,y2) in hand. You can pick the required coordinates you want and use polyarea

[SAJAN Phutela]

Can u please tell how can I feel the area using polyarea? I have not used earlier, thanks please.

[SAJAN Phutela]

@KSSV thanx for you reply, I also did it but in a different manner, please have alook on it

clc;
clear all;

E11=0.041057; 
E12=-0.117734; 
E21=0.029952; 
E22=-0.042564;
A=[1 -E22/E11];
D0=E11*E22-E12*E21 ;

xmax=5; ymax=20;

F1=@(x,y) E11.^2*y.^2+E22.^2*x.^2+(2*x.*y.*E11.*E22-4.*x.*y.*D0);
F2=@(x,y) y-max(A)*x;
Q1=linspace(0,xmax,500); Q2=linspace(0,ymax,500); 
[X,Y]  = meshgrid(Q1,Q2) ;               
G1 = F1(X,Y) ; %Evaluate the value of functions at grid points
G2=  F2(X,Y) ;
[row1,col1] =find(G1>0 & G2>0); % returns the indexing of grid points where conditions are satisfied
row2=col1; col2=row1; % returns the intices of in x and y
X1=Q1(row2); Y1=Q2(col2); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
plot(X1,Y1,'.b','MarkerSize',5)
hold on
fimplicit(F1,[0 7 0 20],'-r','linewidth',1.5)
fimplicit(F2,[0 7 0 20],'-g','linewidth',1.5)

 
 xlim([0,xmax])
ylim([0,ymax])