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AP EAMCET201823 Apr 2018Morning ShiftMathematicsParabolaActual

For the parabola y^2+6 y-2 x+5=0 , match the items in List-I with the suitable item in List-II given below: The correct matching is I II III IV

Options

  1. AF A E C
  2. BF A C E
  3. CA B C D
  4. DF A C D

Correct answer

B. F A C E

Step-by-step solution

Parabola, y^2+6 y-2 x+5=0 array ll & y^2+6 y=2 x-5 & y^2+6 y+9=2 x-5+9 array array ll & (y+3)^2=2(x+2) & Y^2=2 X array (where, Y=y+3 and X=x+2 ) This parabola is in the form of y^2=4 a x by comparing aligned & 4 a=2 & a= 1 2 & Vertex =(0,0) & x+2=0 and y+3=0 & x=-2 and y=-3 & So, vertex (-2,-3) & Focus =(a, 0) & (x+2, y+3)= ( 1 2 , 0 ) & x+2=1 / 2 and y+3=0 & x=- 3 2 , y=-3 & aligned So, focus (- 3 2 ,-3 ) . Equation of directrix, array cc & X=-a & x+2=- 1 2 x= -1 2 -2 & x= -5 2 & 2 x+5=0 array Equation of axis, Y=

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