how do i find the minimum of multiple curves that start from different X and the draw it

I have multiple curves each describes somthing, now i need to pick the minimum between them, the problem is they start from different point in x, I understand what needs to be done but can't seem to figure out how exactly

here is a picture and the code

clc

clear

S=input('Input Apparent Power \n' );

Pm=input('Input Mechanical Power \n');

V=input('Input Rated Voltage \n');

X=input('Input Synchronous Reactance \n');

E=input('Input Maximum Excitation \n');

M=input('Input Stability Margin in percentage \n');

%margin=(100-M)/100

% Apparent Power

theta=0 : 0.01 : 180;

xc=S*cosd(theta);

yc=S*sind(theta);

plot(xc,yc)

% Rotor Limitation

c2=V^2/X;

theta=0 : 0.01 : 90;

xc2=((E*V)/X)*cosd(theta)-c2;

yc2=((E*V)/X)*sind(theta);

% Mechanical Power

xp=min(-3):2;

yp=xp.^0*Pm;

% Margin

for i=1:(((E*V)/X)*10+2)

ym(i)=((i-1)/10)-((i-1)/10)*(M/100);

xm(i)=sqrt(((i-1)/10)^2-ym(i)^2)-c2;

end

maxy1=max(yc);

maxy2=max(yc2);

maxy3=max(yp);

maxy4=max(ym);

arr=cat(4,maxy1,maxy2,maxy3,maxy4);

miny=min(arr,[],4)

maxy=max(arr,[],4)

plot(xp,yp,xc,yc,xc2,yc2,xm,ym)

ylim([0 , maxy+0.1])

Answer 1

[Ive J]

Here and here.