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AP EAMCET20225 Jul 2022Morning ShiftMathematicsStraight LinesActual

The locus of mid-points of points of intersection of x +y =1 with the coordinate axes is

Options

  1. Ax^2+y^2=4
  2. B1 x^2 + 1 y^2 = 4
  3. C1 x^2 + 1 y^2 = 1 2
  4. Dx^2+y^2=2

Correct answer

B. 1 x^2 + 1 y^2 = 4

Step-by-step solution

Let the line cut the axes in A and B and if (h, k) be the mid-point of A B , then 2 h= 1 , 2 k= 1 In order to find the locus, eleminate the variable by ^2 + ^2 =1 1 4 h^2 + 1 4 k^2 =1 1 x^2 + 1 y^2 =4

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