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BITSAT2010MathematicsEllipseActual

If the line (2 x-1=0 ) is the directrix of the parabola (y^2-k x+6=0 ), then one of the values of (k ) is

Options

  1. A-6
  2. B6
  3. C(1 / 4 )
  4. D(-1 / 4 )

Correct answer

A. -6

Step-by-step solution

Given equation of parabola is (y^2-k x+6=0 ) ( y^2=k x-6 y^2=k (x- 6 k ) ) Now, directrix, (x- 6 k =- k 4 ) ( x= 6 k - k 4 ) ...(i) But directrix is given ( x= 1 2 ) ...(ii) ( aligned & 6 k - k 4 = 1 2 24-k^2=2 k & k^2+2 k-24=0 & (k+6)(k-4)=0 k=-6, k=4 aligned )

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