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AP EAMCET202124 Aug 2021Evening ShiftMathematicsStraight LinesActual

A straight rod of length 4 units slides such that its ends A and B always lie on the X and Y -axes respectively. Then, the locus of the centroid of O A B is

Options

  1. Ax^2+y^2=4
  2. Bx^2+y^2=3
  3. Cx^2+y^2= 9 16
  4. Dx^2+y^2= 16 9

Correct answer

D. x^2+y^2= 16 9

Step-by-step solution

Let the coordinate of vertices of O A BO=(0,0) A=(x, 0) and B=(0, y)(h, k) is centroid of O A B . h= x 3 and k= y 3 aligned & x=3 h and y=3 k & x=3 h and y=3 k aligned Given, x^2+y^2=16x^2+y^2=9 (h^2+k^2 ) 16 9 =h^2+k^2 Locus of centroid of O A B is x^2+y^2=16 / 9

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