anyway to find common tangent for two functions

Hi:

I have two functions, and I want to find a tangent circle with a given radius, for example, function y=0.5*x and y=x^2, is there anyway to achieve this in Matlab?

code to plot the figure is shown below:

x=0:0.01:1;
y1=0.5*x;
y2=x.^3;
f=figure('color','w');
hold on
plot(x,y1)
plot(x,y2)

Thanks!

Yu

Answer 1

[Matt J]

The problem has 6 unknowns, the (xc,yc) coordinates of the circle center and the (x,y) coordinates of each point of tangency. Each point of tangency must satisy 3 equations, the equation for the curve, the equation for the circle, and the equation that matches their derivatives. You can therefore write down 6 equations in 6 unknowns and solve them with fsolve.