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AP EAMCET2012MathematicsParabola

Let x+y=k be a normal to the parabola y^2=12 x . If p is length of the perpendicular from the focus of the parabola onto this normal, then 4 k-2 p^2 is equal to

Options

  1. A1
  2. B0
  3. C-1
  4. D2

Correct answer

B. 0

Step-by-step solution

Given equation of parabola is y^2=12 x Here, a=3 Equation of normal is aligned y & =m x-2 a m-a m^3 ( m=-1) y & =-x-2(3)(-1)-3(-1)^3 & =-x+6+3 aligned But given normal is aligned & x+y=k & k=9 & aligned Focus of a given parabola is S(3,0) . Now, perpendicular distance from S(3,0) to the line (i) is aligned & p= |3(1)+0-9| 1^2+1^2 = 6 2 4 k-2 p^2 & =4(9)-2 ( 6 2 )^2 & =36-2 36 2 =0 aligned

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