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For the parabola y= h^3 3 x^2+ h^2 2 x-h+ 3 4 h^3 if the equation of directrix is y=k , then k: h

Options

  1. A16: 19
  2. B-19: 16
  3. C20: 27
  4. D-27: 20

Correct answer

B. -19: 16

Step-by-step solution

Given, y= h^3 3 x^2+ h^2 2 x-h+ 3 4 h^3 12 h^3 y=4 h^6 x^2+6 h^5 x-12 h^4+94 h^6 x^2+6 h^5 x=12 h^3 y+12 h^4-9 (x^2+ 3 2 h x )= 12 h^4 4 h^6 (y+ 12 h^4 12 h^3 - 3 14 h^3 ) (x^2+ 3 2 h^2 + 3 16 h^2 )= 3 h^3 (y+h- 3 4 h^3 )+ 9 16 h^2 (x+ 3 2 h )^2= 3 h^3 (y+ 19 h 16 - 3 4 h^3 ) Here, a= 3 4 h^3 Equation of directrix is y+ 19 h 16 - 3 4 h^3 = -3 4 h^3 y=- 19 h 16 k=- 19 h 16 k h =- 19 16 k: h=-19: 16

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