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AP EAMCET2005MathematicsParabola

The parabola with directrix x+2 y-1=0 and focus (1,0) is

Options

  1. A4 x^2-4 x y+y^2-8 x+4 y+4=0
  2. B4 x^2+4 x y+y^2-8 x+4 y+4=0
  3. C4 x^2+5 x y+y^2+8 x-4 y+4=0
  4. D4 x^2-4 x y+y^2-8 x-4 y+4=0

Correct answer

A. 4 x^2-4 x y+y^2-8 x+4 y+4=0

Step-by-step solution

Let P(x, y) be any point on the parabola By definition of Parabola P M=P S x+2 y-1 1+4 = (x-1)^2+y^2 On squaring both sides, we get gathered x^2+4 y^2+1+4 x y-4 y-2 x =5 (x^2+1-2 x+y^2 ) 4 x^2+y^2-8 x+4 y-4 x y+4=0 gathered

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