Curvature problem from class

Let . Consider the level curve given by setting . We wish to find a graph the tangent circle at the point (1,1). In class we showed that if define the function y=f(x) implicitly we can compute to get y'=-3/4, y''=17/32, hence get K=.0906721... . Now the radius of the tangent circle is r=1/K.

But where is the center? Let r be the vector from the point (1,1) to the center. Construct another vector, v , tangent to the curve y=f(x) at (1,1). Now, v dot r = 0 and | r | = 1/K. This allows us to find r and then the center is r + <1,1>.

> cu:=plots[implicitplot] (y^3*x+x^2*y-2=0,x=-10..10,y=-10..10,
numpoints=5000,color=black,thickness=3):

> r:=1/(.0906721);

> c := plottools[circle]([1+3*r/5,1+12*r/15], r, color=red):

> plots[display](cu,c);

>