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AP EAMCET201920 Apr 2019Evening ShiftMathematicsParabolaActual

The vertex and the focus of the parabola 2 y^2+5 x-6 y+1=0 are respectively

Options

  1. A( 7 10 , 3 2 ), ( 3 40 , 3 2 )
  2. B( -7 10 , 3 2 ), ( 53 40 , 3 2 )
  3. C( 7 10 , -3 2 ), ( 7 10 , 7 8 )
  4. D( -7 10 , -3 2 ), ( 7 10 , 17 8 )

Correct answer

A. ( 7 10 , 3 2 ), ( 3 40 , 3 2 )

Step-by-step solution

Equation of given parabola is aligned & 2 y^2+5 x-6 y+1=0 & 2 (y^2-3 y )+5 x+1=0 & 2 (y^2-3 y+ ( 3 2 )^2- ( 3 2 )^2 )+5 x+1=0 & 2 (y- 3 2 )^2- 9 2 +5 x+1=0 & 2 (y- 3 2 )^2=-5 (x- 7 10 ) aligned The coordinate of vertex of parabola (i) is ( 7 10 , 3 2 ) and coordinate of focus of parabola (i) is aligned (- 5 8 + 7 10 , 3 2 ) & = ( -50+56 80 , 3 2 ) & = ( 6 80 , 3 2 ) or ( 3 40 , 3 2 ) aligned Hence, option (a) correct.

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