why the command does not work:** _EnvHorizontalName := x;_EnvVerticalName := y**?

And a few lines later asks me the name of the axes

restart;

with(plots); with(plottools);

The circle S with center at the origin and radius 2 is given by the equation x2 + y2 = 4

The circle S have two tangents passing through the point (4, 1). Find the equation for each of them.

x^2+y^2 = 4;

subs(y(x) = y, solve(diff(subs(y = y(x), x^2+y^2 = 4), x), diff(y(x), x)));

y-1 = -x*(x-4)/y;

x^2+y^2 = 4, y-1 = -x*(x-4)/y;

solve({y-1 = -x*(x-4)/y, x^2+y^2 = 4}, {x, y});

allvalues({x = 1-RootOf(17*_Z^2-2*_Z-3), y = 4*RootOf(17*_Z^2-2*_Z-3)});

cp1 := eval([x, y], %[1]);

cp2 := eval([x, y], `%%`[2]);

graph1 := implicitplot(x^2+y^2 = 4, x = -3 .. 3, y = -3 .. 3);

extp := point([4, 1], color = black, symbol = cross, symbolsize = 25);

ccp1 := point(cp1, color = green, symbolsize = 25, symbol = circle);

ccp2 := point(cp2, color = green, symbolsize = 25, symbol = circle);

tl1 := line([4, 1], cp1, color = red, linestyle = solid, color = blue);

tl2 := line([4, 1], cp2, color = red, linestyle = solid, color = blue);

display([graph1, extp, ccp1, ccp2, tl1, tl2]);

with(geometry);

_EnvHorizontalName := x;_EnvVerticalName := y;

point(Ex, 4, 1), point(A, cp1[1], cp1[2]), point(B, cp2[1], cp2[2]);

line(t1, [Ex, A]);

line(t2, [Ex, B]);

map(detail, [t1, t2]);

Equation(t1);

Equation(t2);

ll1 := implicitplot(Equation(t1), x = -3 .. 5, y = -3 .. 3, color = black);

ll2 := implicitplot(Equation(t2), x = -3 .. 5, y = -3 .. 3, color = black);

display([graph1, extp, ccp1, ccp2, ll1, ll2]);

Tangentlinrev.mw