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Question: How do I draw an implicit function accompanied by several tangent lines and the points?

Question:How do I draw an implicit function accompanied by several tangent lines and the points?

Vahid_math 15 Maple 18
implicit
December 17 2018
1

I have written the following commands in Maple 18.

implicit_func := x^3+y^3 = 9*x*y;
c := 2;
s := evalf(solve(subs(x = c, implicit_func)));
m1 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[1]}));
                          0.8000000000
m2 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[2]}));
                          -1.257321410
m3 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[3]}));
                          0.4573214099

How can I graph all "implicit_func, y - s[1] = m1*(x-c), y - s[2] = m2*(x-c), y - s[3] = m3*(x-c), and the points (c,s[1]), (c,s[2]), and (c,s[3])" in a plane? (Each of them in a different color)     
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