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AP EAMCET202125 Aug 2021Evening ShiftMathematicsStraight LinesActual

A rod of length 2l slides with its ends on two perpendicular lines, then the locus of its mid-point is

Options

  1. Ax^2+y^2=l^2
  2. Bx^2-y^2=l^2
  3. C2x^2+2y^2=l^2
  4. D2x^2-2y^2=l^2

Correct answer

A. x^2+y^2=l^2

Step-by-step solution

Based on given information, diagram is drawn. Let D be the point on rod. Let x=2 and y=2 In A O B , aligned x^2+y^2 & =(2 l)^2 (2 )^2+(2 )^2 & =4 l^2 ^2+ ^2 & =l^2 x^2 4 + y^2 4 & =l^2 aligned x^2+y^2=4 l^2 array l x=2 =x / 2 y=2 =y / 2 array .

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