$y=f(x)$ and $x=g(y)$ are two curves and $P(x, y)$ is a common point of the two curves. If at $P$, on the curve $y=f(x), \frac{d y}{d x}=Q(x)$ and at the same point $P$ on the curve $x=g(y), \frac{d x}{d y}=-Q(x)$, then

• A

  the two curves have a common tangent
• B

  the angle between two curves is $45^{\circ}$
• Correct answer
  C

  tangent drawn at $P$ to one curve is normal to the other curve at $P$
• D

  the two curves never intersect orthogonally

Hence, the correct answer is option: 'C'.