Consider a circle c and an angle <(HIJ). Take a point M on the circle c and build the angle <(MKN) equal to <(HIJ). Consider a point O on MN such that the ratio OM/ON = m remains constant.
Construct P by the recipe KP = (KM)*(KN)*(KO) (as complex numbers). Then take Q on OP such that QP/QO = n remains constant.
The locus of Q as M moves on the circle c is curve k.
Switch to the "Select on contour" tool (Ctrl+2) and pick-move point O (changing the ratio m). The ratio OK/OP remains fixed, the curve k transforms to a similar one.
Pick-move point Q on OP (changing the ratio n). The curve k changes its shape. However the curve (modulo similarity) does not depend on the measure of angle <(JIH). Though it depends on the radius of the circle c.
![[alogo]](alogo.png){kind=small}
An Algebraic Locus ![[0_0]](Algebraic_Locus_files/Algebraic_Locus_0_0_0.png)
![[0_1]](Algebraic_Locus_files/Algebraic_Locus_0_0_1.png)
![[0_2]](Algebraic_Locus_files/Algebraic_Locus_0_0_2.png)
![[1_0]](Algebraic_Locus_files/Algebraic_Locus_0_1_0.png)
![[1_1]](Algebraic_Locus_files/Algebraic_Locus_0_1_1.png)
![[1_2]](Algebraic_Locus_files/Algebraic_Locus_0_1_2.png)