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If y=f(x) is a curve and if there exists...

If `y=f(x)` is a curve and if there exists two points `A(x_(1),f(x_(1)) and B(x_(2),f(x_(2))` on it such that `f'(x_(1))=-(1)/(f'(x_(2)))=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1))`, then the tangent at `x_(1)` is normal at `x_(2)` for that curve. Now, anwer the following questions.
Number of such lines on the curve `y^(2)=x^(3)`, is

A

1

B

2

C

3

D

infinite

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