Let $A$ and $B$ be two fixed points on a fixed straight line. Two circles touch this line at $A$ and $B$ respectively and tangent to each other at $M$. When the circles vary, the locus of $M$ forms

• Correct answer
  A

  a circle with diameter $A B$ minus points $A$ and $B$.
• B

  an ellipse with major axis $A B$ minus points $A$ and $B$.
• C

  an ellipse with minor axis $A B$ minus points $A$ and $B$.
• D

  a square with diagonal $A B$ minus points $A$ and $B$.

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