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AP EAMCET202021 Sep 2020Morning ShiftMathematicsParabolaActual

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

Options

  1. A(4 x^2-4 x y+y^2-8 x+4 y+4=0 )
  2. B(4 x^2+4 x y+y^2-8 x+4 y+4=0 )
  3. C(4 x^2+4 x y+y^2+8 x-4 y+4=0 )
  4. D(4 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

Equation of parabola having directrix (x+2 y-1=0 ) and focus ((1,0) ) is ( aligned & |x+2 y-1| 1+4 = (x-1)^2+(y-0)^2 & (x+2 y-1)^2=5 [(x-1)^2+y^2 ] & x^2+4 y^2+1+4 x y-2 x-4 y=5 & (x^2+y^2-2 x+1 ) & 4 x^2-4 x y+y^2-8 x+4 y+4=0 aligned ) Hence, option (a) is correct.

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