clear;

% problem 1a

x = -1 : 0.1 : 7;
s = sqrt(16-(x-3).^2);
yp = -1 + s;
ym = -1 - s;

figure(1);
plot(x,yp,'g-');
hold on;
plot(x,ym,'g-');
axis equal;
xlabel('x');
ylabel('y');


% problem 1b
t = 0 : 0.1 : 6.3;
x =  3 + 4 * cos(t);
y = -1 + 4 * sin(t);
figure(2);
plot(x,y,'m-');
axis equal;
xlabel('x');
ylabel('y');


% problem 2
x = [-1 0 2 3 4  5];
y = [ 1 2 4 3 10 7];
co = polyfit(x,y,length(x)-1);

xx = min(x) : 0.1 : max(x);
yy = polyval(co,xx);
figure(3);
plot(xx,yy,'r-');
hold on;
plot(x,y,'ko');
xlabel('x');
ylabel('y');