ψ ψ point

Geometry Level 4

Given a curve M : { ( x , y ) ∣ y = x 2 } M:\left\{(x,y)|y=x^2\right\} ,now give the definition of ψ ψ point:

For a point A ∈ M A\in M , ∃ B ∈ M , C ∈ M \exists B\in M,C\in M ,such that ∣ A B → ∣ = ∣ A C → ∣ , A B → ⋅ A C → = 0 |\overrightarrow{AB}|=|\overrightarrow{AC}| , \overrightarrow{AB}\cdot\overrightarrow{AC}=0 ,then point A A is a ψ ψ point on the curve M M .

Which statement is true ?

There is only one ψ ψ point on the curve M. There are infinite ψ ψ points on the curve M,but not all the points on the curve. All the points on the curve M are ψ ψ points. There are finite ψ ψ points on the curve M. There is no ψ ψ points on the curve M.

Alice Smith by Alice Smith , 20, China

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