% Parameters
p0 = 400; % Initial p0 value
M = 1.5; % Ratio for the ellipse equation
% Linear line equation
x1 = 400:0.1:600;
yeta = 3 * x1 - 1200;
% Plot the static linear line
figure;
subplot(2, 2, 1);
plot(x1, yeta, 'r', 'LineWidth', 1.5);
hold on;
% Initial plot for the first ellipse
t = 0:0.01:pi;
p_values = p0/2 + p0/2 * cos(t);
q_values = p0/2 * M * sin(t);
plot(p_values, q_values, 'k', 'LineWidth', 1.5);
hold on;
% Plot ellipse and calculate intersections in a loop
for k = 1:5
p0 = p0 + 10; % Increase p0 for the growing ellipse
p_values = p0/2 + p0/2 * cos(t);
q_values = p0/2 * M * sin(t);
% Plot the growing ellipse
plot(p_values, q_values, 'k', 'LineWidth', 1.5);
% Find intersections
for i = 1:length(x1)
% Intersection condition
idx = find(abs(p_values - x1(i)) < 1e-1 & abs(q_values - yeta(i)) < 1e-1);
if ~isempty(idx)
plot(p_values(idx), q_values(idx), 'ko', 'MarkerFaceColor', 'k', 'MarkerSize', 4);
end
end
end
% Set axis properties
axis equal;
xlim([350 650]);
ylim([0 250]);
xlabel('p [kPa]');
ylabel('q [kPa]');
title('Intersections of Ellipses and Linear Line');
grid on;
hold off;
