a=1;
c=a/sqrt(2);

t=linspace(0,2*pi,200);
x=cos(t)./(1+sin(t).^2);
y=cos(t).*sin(t)./(1+sin(t).^2);
hold on
plot(x,y,"b",'LineWidth', 2)

% plot X and Y axis
x=[-1.2*a, 1.2*a]; y=[0, 0]; line(x,y)
x=[0, 0]; y=[-a*3/5, a*3/5]; line(x,y)

% plot focal points
x=[-c, c]; y=[0, 0];
plot(x,y,"ko","linestyle","none","markerfacecolor", "k")

hold off

axis([-1.2*a,1.2*a,-a*3/5,a*3/5],"equal","on")

% turn on grid
grid on