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Question: where the vertex of an angle moves ?

Question:where the vertex of an angle moves ?

JAMET 410 Maple 2018
February 10 2020
1
restart; with(plots); _EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; para := -2*p*x+y^2 = 0; para1 := -2*p1*x+y^2 = 0; t := y-m*x-p/(2*m) = 0; t1 := y+x/m+(1/2)*p1*m = 0; sol := op(solve([t, t1], [x, y])); eliminate({rhs(sol[1]), rhs(sol[2])}, m); for example : m := 2; p := 1; p1 := -2; PARA := implicitplot(para, x = -3 .. 3, y = -3 .. 3, color = blue); PARA1 := implicitplot(para1, x = -3 .. 3, y = -3 .. 3, color = green); Tang := implicitplot(t, x = -3 .. 3, y = -3 .. 3, color = brown); Tang1 := implicitplot(t1, x = -3 .. 3, y = -3 .. 3, color = aquamarine); NULL; #m is not constant display([PARA, PARA1, Tang, Tang1], view = [-3 .. 3, -3 .. 3], scaling = constrained);#on what curve is the vertex of the angle of 2 tangents ? Thank you.
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