# Weird calculus problem

1. Jan 7, 2004

### 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

2. Jan 7, 2004

### 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
$$f(x)=\frac{x^3}{3}+C$$