(%i1)

I:[cos(phi+%pi/2),sin(phi+%pi/2)];

(%i2)

R(alpha):=matrix([cos(alpha),sin(alpha)],[-sin(alpha),cos(alpha)]);

(%i3)

nd:matrix([0,1]);

(%i4)

nr(alpha):=nd.R(alpha);

(%i5)

nr:[nr(2*phi)[1,1],nr(2*phi)[1,2]];

(%i6)

l(phi):=(x-I[1])*nr[1]+(y-I[2])*nr[2]=0;

(%i7)

ld(phi):=diff(l(phi),phi);

(%i8)

l(phi); ld(phi);

(%i10)

Curve:trigreduce(solve([l(phi)=0,ld(phi)=0],[x,y]));

(%i11)

wxplot2d([parametric,rhs(Curve[1][1]),rhs(Curve[1][2]),[phi,0,2*%pi], [nticks,400]],[x,-1,1],[y,-1,1],[gnuplot_preamble,"set size ratio 1;"]);

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Created with wxMaxima.