f = -7 (slider from -10 to 10, step 0.1)
e = 2 (slider from -10 to 10, step 0.1)
d = 1 (slider from -10 to 10, step 0.1)
c = 0 (slider from -10 to 10, step 0.1)
b = 0 (slider from -10 to 10, step 0.1)
a = 1 (slider from -10 to 10, step 0.1)
A = (1.0353792472926022, -2.916100188632113)
A', text1 = Affine(A, a, b, c, d, e, f)
M = (4.753633917424496, 1.5458054155261596)
K = (8.153181044402228, 2.2894563495525384)
k = Circle(M, K)
E = Point(k)
F = Point(k)
G = Point(k)
H = Point(k)
K', text2 = Affine(K, a, b, c, d, e, f)
E', text3 = Affine(E, a, b, c, d, e, f)
F', text4 = Affine(F, a, b, c, d, e, f)
G', text5 = Affine(G, a, b, c, d, e, f)
H', text6 = Affine(H, a, b, c, d, e, f)
k' = Conic(K', E', F', G', H')
M', text7 = Affine(M, a, b, c, d, e, f)
G_1 = (-6.401130092971186, 6.857597801428865)
G_2 = (-8.84455459048643, 0.9083903292178349)
g = Line(G_1, G_2)
G'_1, text8 = Affine(G_1, a, b, c, d, e, f)
G'_2, text9 = Affine(G_2, a, b, c, d, e, f)
g' = Line(G'_2, G'_1)

Tool: Affine Transformation (command Affine)
Point, 6 numbers:a1,a2,b1,b2,c1,c2
Input: A, a_1, a_2, b_1, b_2, c_1, c_2
Output: A', T1

u = Vector((c_1, c_2))
A': (a_1 x(A) + b_1 y(A), a_2 x(A) + b_2 y(A)) + u
T1: "\left(\begin{array}{cc}" + a_1 + "&" + b_1 + "\\" + a_2 + "&" + b_2 + "\end{array}\right)\left(\begin{array}{cc}" + (x(A)) + "\\" + (y(A)) + "\end{array}\right)+\left(\begin{array}{cc}" + c_1 + "\\" + c_2 + "\end{array}\right)=\left(\begin{array}{cc}" + (x(A')) + "\\" + (y(A')) + "\end{array}\right)"