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AP EAMCET202317 May 2023Evening ShiftMathematicsParabolaActual

Let 1 be the directrix of the parabola 9 y^2+12 y+9 x-14=0 and l₁ be the line passing through the vertex of this parabola and the origin. If ( h , k ) is the point of intersection of l and l₁ , then h + k =

Options

  1. A-9 / 2
  2. B3 / 2
  3. C-3 / 4
  4. D9 / 4

Correct answer

A. -9 / 2

Step-by-step solution

Given: 9 y^2+12 y+9 x-14=0 (y+ 2 3 )^2=-4 1 4 (x-2) Whose vertex is (- 2 3 , 2 ) Equation of line passing through (- 2 3 , 2 ) and (0,0) : (y-0)= 2-0 - 2 3 -0 (x-0) y=-3 x Now, the equation of directrix of parabola (i) is x= 1 4 +2 x= 9 4 ...(iii) Solving eq ^ n (ii) & (iii), we get x= 9 4 and y=- 27 4 h= 9 4 & k=- 27 4 So, h+k= 9 4 - 27 4 = -18 4 = -9 2

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