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AP EAMCET2011MathematicsCircle

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

Options

  1. Ax^2+y^2=4 a^2
  2. Bx^2+y^2=2 a x
  3. Cx^2+y^2=2 a y
  4. Dx^2+y^2=2 a x+2 a y

Correct answer

C. x^2+y^2=2 a y

Step-by-step 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 aligned x^2+y^2 & =(2 a)^2 x^2+y^2 & =4 a^2 aligned

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