A line segment $A M=a$ moves in the $X O Y$ plane such that $A M$ is parallel to the $X$-axis. If $A$ moves along the circle $x^2+y^2=a^2$, then the locus of $M$ is

• A

  $x^2+y^2=4 a^2$
• B

  $x^2+y^2=2 a x$
• Correct answer
  C

  $x^2+y^2=2 a y$
• D

  $x^2+y^2=2 a x+2 a y$

Solution

The given equation of circle, $x^2+y^2=a^2$ and length of $A M=a$
Now, total length $O M=O A+A M=2 a$ Since, point $A$ moves along the circle, so it describes a circle with radius $O M=2 a$, whose equation is $\begin{aligned} x^2+y^2 & =(2 a)^2 \\ x^2+y^2 & =4 a^2 \end{aligned}$

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