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AP EAMCET202316 May 2023Evening ShiftMathematicsParabolaActual

Let Z be the point of intersection of the axis and the directrix of the parabola 4 x^2-12 x+4 y+5=0 . If S is its focus, then the point which divides SZ in the ratio 2: 1 is

Options

  1. A( 3 2 , 13 12 )
  2. B(1, 13 12 t)
  3. C( 3 4 , 13 4 )
  4. D( 3 2 , 13 4 )

Correct answer

A. ( 3 2 , 13 12 )

Step-by-step solution

Given equation of parabola is 4 x^2-12 x+4 y+5=0 aligned & i.e (x- 3 2 )^2=-(y-1) vertex = ( 3 2 , 1 ) & Z= (0+ 3 2 , 1 4 +1 )= ( 3 2 , 5 4 ) & and focus (s)= (0+ 3 2 ,- 1 4 +1 )= ( 3 2 , 3 4 ) & Now, required point = ( 6 2 2 + 3 2 , 10 4 + 3 4 )= ( 3 2 , 13 12 ) aligned

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