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MHT CET202526 Apr 2025Morning ShiftMathematicsParabolaActual

The equation of the directrix of the parabola y^2+4 y+4 x+2=0 is

Options

  1. Ax=-1
  2. Bx=1
  3. Cx= -3 2
  4. Dx= 3 2

Correct answer

D. x= 3 2

Step-by-step solution

Finding the directrix of the parabola defined by y²+4y+4x+2=0. Rewriting the equation by completing the square for the y-terms: y^2+4y+4 = -4x-2+4 , resulting in (y+2)^2 = -4x+2 . Factoring the right side yields (y+2)^2 = -4(x - 1/2) . This matches the standard form (y-k)^2 = -4a(x-h) , with vertex at (1/2, -2) and a=1 . The directrix for this left-opening parabola is x = h+a = 1/2 + 1 = 3/2 . Final answer: x = 3/2

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