Imagine the quadratic curve with equation
On the concave side of this curve there is a circle of radius R. The circle is as close the the extremum of the quadratic as possible without resulting in the curves crossing each other. Write a function which takes as inputs a,b,c, and R and returns the coordinates of the center of the circle.
For example, if
a=1; b=0; c=10; R=pi;
then the function returns
T = circ_puzz(a,b,c,R) T = 0 20.1196044010894
This can be visualized as follows:
P = @(x) a*x.^2 + b*x + c; % Quadratic C = @(x) real(-sqrt(R^2-(x-T(1)).^2) + T(2)); % Lower half circle x = linspace(-R,R,10000); % Range of plotted data. plot(x,C(x),'r',x,-C(x)+2*T(2),'r',x,P(x),T(1),T(2),'*k') ylim([0,30]) axis equal