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Manipal MET2015MathematicsParabola

If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then one of the value of k is

Options

  1. A1 8
  2. B8
  3. C4
  4. D1 4

Correct answer

C. 4

Step-by-step solution

Given equation of parabola is y^2-k x+8=0 array lr & y^2=k (x- 8 k ) & (y-0)^2=k (x- 8 k ) array The equation of the directrix of this parabola is x- 8 k =- k 4 [ x=-a] x= 8 k - k 4 But the equation of the directrix is given as x-1=0 . 8 k - k 4 =1 aligned & & k^2+4 k-32 & =0 & & (k-4)(k+8) & =0 & & k & =-8,4 aligned

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