If the circles $x^2+y^2+5 k x+2 y+k=0$ and $2 x^2+2 y^2+2 k x+3 y-1=0, k \in R$ intersect at points $P$ and $Q$, then the line $4 x+5 y-k=0$ passes through $P$ and $Q$ for

• A

  exactly one value of $k$
• B

  exactly two values of $k$
• Correct answer
  C

  no value of $k$
• D

  infinitely many values of $k$

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