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Consider the two curves C1: y^2=4x ,C2: ...

Consider the two curves `C_1: y^2=4x ,C_2: x^2+y^2-6x+1=0` . Then `C_1` and `C_2` touch each other only at one point `C_1` and `C_2` touch each other exactly at two point `C_1` and `C_2` interesect (but do not touch) at exactly two points. `C_1` and `C_2` neither intersect nor touch each other.

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