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AP EAMCET202125 Aug 2021Evening ShiftMathematicsParabolaActual

The equation of the directrix of parabola y^2-x+4 y+5=0 is

Options

  1. A4y − 3 = 0
  2. B4x − 3 = 0
  3. C3x − 4 = 0
  4. D3y − 4 = 0

Correct answer

B. 4x − 3 = 0

Step-by-step solution

Given parabola is aligned y^2-x+4 y+5 & =0 y^2+4 y & =x-5 y^2+4 y+4 & =x-5+4 (y+2)^2 & =(x-1) aligned On comparing with general form of parabola aligned & (y-k)^2=4 a(x-h) & or Y^2=4 a X & where Y=y-k & X=x-h & Vertex (h, k)=(1,-2) & and a= 1 4 aligned Since, equation of directrix is X = − a array ll & x-1=-1 / 4 & x=1-1 / 4=3 / 4 & 4 x-3=0 array

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