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AP EAMCET201823 Apr 2018Evening ShiftMathematicsParabolaActual

If a parabola passess through the points (-2,1) , (1,2) and (-1,3) having horizontal axis, then the length of the latus rectum of that parabola is

Options

  1. A5
  2. B5 2
  3. C2 5
  4. D1 5

Correct answer

C. 2 5

Step-by-step solution

Let the equation of parabola having horizontal axis, vertex at (h, k) is (y-k)^2=4 a(x-h) Parabola (i) passes through the points (-2,1) , (1,2) and (-1,3) , so aligned & (k-1)^2=4 a(-2-h) & k^2-2 k+1=-8 a-4 a h & (k-2^2=4 a(1-h) . & k^2-4 k+4=4 a-4 a h & and (3-k)^2=4 a(-1-h) & k^2-6 k+9=-4 a-4 a h & aligned From Eqs. (ii), (iii) and (iv), we get 4 a= 2 5

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