Weird calculus problem

[tandoorichicken]

Which of the following is an equation of a curve that intersects at right angles every curve of the family y = 1/x + k where k takes all real values?
a)y= -x b)y= -x^2 c)y= -x^3/3 d)y=x^3/3 e)y=ln x

[NateTG]

Are you sure that you don't mean
y=\frac{1}{x} + k

then \frac{dy}{dx}=\frac{-1}{x^2}

any suitable function would have the negative reciprocal slope, so
\frac{df}{dx}=\frac{x^2}{1}=x^2
sp
f(x)=\frac{x^3}{3}+C

and the answer is d.